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USC Computer Science Technical Reports, no. 770 (2002)

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USC Computer Science Technical Reports, no. 770 (2002)

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Content 1 Small Large-Scale Wireless Networks: Mobility-
Assisted Resource Discovery
Ahmed Helmy
Department of Electrical Engineering
University of Southern California
helmy@usc.edu
Abstract - In this study, the concept of small worlds is
investigated in the context of large-scale wireless ad hoc and
sensor networks. Wireless networks are spatial graphs that are
usually much more clustered than random networks and have
much higher path length characteristics. We observe that by
adding only few random links, path length of wireless networks
can be reduced drastically without affecting clustering.
What is even more interesting is that such links need not be
formed randomly but may be confined to a limited number of
hops between the connected nodes. This has an important
practical implication, as now we can introduce a distributed
algorithm in large-scale wireless networks, based on what we
call contacts , to improve the performance of resource discovery
in such networks, without resorting to global flooding.
We propose new contact -based protocols for adding logical
short cuts in wireless networks efficiently. The new protocols
take advantage of mobility in order to increase reachability of
the search. We study the performance of our proposed contact-
based architecture, and clarify the context in which large-scale
wireless networks can be turned into small world networks.
Index terms - Small world graphs, resource discovery, ad hoc
and sensor networks, wireless networks, mobility analysis.
I. I NTRODUCTION
The concept of small worlds was studied in the 60’s
in the context of social networks [1] , during which
experiments of mail delivery using acquaintances
resulted in an average of ‘six degrees of separation’,
i.e., on average a letter needed six acquaintances to be
delivered. Recent research by Watts [2] [3] has shown
that in relational graphs adding a few number of random
links to regular graphs results in graphs with low
average path length and high clustering. Such graphs
are called small world graphs.
Emerging multi-hop wireless networks, such as ad
hoc and sensor networks, do not belong in the category
of relational graphs. Rather, they belong in the category
of spatial graphs, where the links between nodes depend
on the radio range, which in turn is a function of the
distance between the nodes. The applicability of small
world graphs to spatial graphs has not been established
by [2] . In this paper, we attempt to develop a better
understanding of the small world concept in the context
of wireless networks. Specifically, what are the path
length and clustering characteristics of wireless
networks? Can we create networks that have reduced
path length by adding a small number of short cuts? Do
these short cuts have to be totally random? What do
these short cuts represent given the limited radio
connectivity in wireless networks? It would likely
represent logical connections that translate into multiple
physical hops. Finally, given reasonable answers to the
above questions, can we develop network architectures,
for resource discovery, that incur low degrees of
separation between nodes in large-scale wireless
networks?
Our study attempts to provide answers to the above
questions. Under the assumptions of our study, results
in this paper suggest that we can actually reduce the
path length of wireless networks drastically by adding a
few random links (resembling a small world).
Furthermore, these random links need not be totally
random, but in fact may be confined to a small fraction
of the network diameter, thus reducing the overhead of
creating such network.
Based on these observations a new architecture is
introduced that attempts to create a small world in
large-scale wireless networks (with potentially
thousands of nodes). The architecture is based on
defining contacts for network nodes. These contacts are
chosen in a simple and efficient way by taking
advantage of mobility. The goal of such contacts is to
be used during resource discovery without global
flooding.
We analyze the different parameters of our
architecture and evaluate its performance in terms of
network reachability. We also specify a new set of
mobility-based protocols for efficient contact selection.
We evaluate our proposed protocols under mobility
conditions. Initial results indicate promise for efficient
contact selection, and we propose several favorable
protocol settings based on our analysis. In future work,
we plan to conduct more detailed evaluations using
different mobility models and richer metrics. We shall
also investigate other heuristics for contact selection.
2 The rest of the paper is outlined as follows. Section II
provides background on small world concept and
outlines our work in that area. Section III presents
experiments and results for small world wireless
networks. Section IV provides a link between our small
world analysis and resource discovery in wireless
networks. Section V presents related work in the area of
resource discovery. Section VI introduces our contact-
based architecture. Section VII introduces and analyzes
a new class of mobility-based contact selection
protocols. Section VIII concludes and discusses future
work.
II. S MALL WORLDS
The small world phenomenon comes from the
observation that individuals are often linked by a short
chain of acquaintances. Milgram [1] conducted a series
of experiments to study social contacts and networks. In
his experiments, individuals were randomly chosen to
deliver letters between Nebraska and Massachusetts, the
source can only deliver the letter through acquaintances
knowing the target’s address and occupation. It was
found that an average of ‘six degrees of separation’
exists between senders and receivers. This provided an
interesting yet intriguing result. What is the structure of
social networks that allows to create a small number of
degrees of separation within a very large population? In
an effort to further understand such structure Watts [2]
conducted a set of re-wiring experiments on graphs
ranging from regular graphs to random graphs. It was
observed that by re-wiring a few random links in
regular graphs, the average path length was reduced
drastically (approaching that of random graphs), while
the clustering
1 remains almost constant (similar to that
of regular graphs). This class of graphs was termed
small world graphs , and it emphasizes the importance
of the random links acting as short cuts that contract the
average path length of the graph. The experiment was
conducted for relational graphs, in which links are not
restricted by distance between the nodes. It was also
noted that for spatial graphs, in which links are a
function of the distance between nodes, the small world
phenomenon does not exist (that is, path length and
clustering curves almost match)
2 . According to the

1 By clustering we refer to the clustering coefficient that basically captures
the fraction of nodes’ neighbors that are also neighbors of each other.
Clustering refers in some sense to the underlying structure of the network.
2 Some of Watts’ experiments were conducted on 1-dimentional spatial
graphs, in which k links, on average, originate from every node. Links for all
experiment, in such graphs it is hard to add short cuts
while maintaining clustering.
Multi-hop wireless networks, including ad hoc and
sensor networks belong to the class of spatial graphs,
where the links are determined by the radio
connectivity, which is a function of distance. Hence, we
expect that such networks, by their own nature, do not
lend themselves to small worlds. We also expect high
clustering in wireless network due to the locality of the
links, since many of a node’s neighbors may be
neighbors of each other too. Also, due to this locality
we expect the path length for such networks to be high
as compared to randomly connected networks.
In this work, we conduct further experiments on
spatial graphs in the context of multi-hop wireless
networks, and investigate the applicability of the small
world concept to these networks. Our study takes a
practical perspective in which we hope to utilize small
worlds in designing efficient protocols for ad hoc and
sensor networks. In particular, we propose a novel
contact-based architecture for resource discovery in
large-scale ad hoc and sensor network. In such
architecture, our goal is to reduce the number of queries
during the search for a target node or resource. The
distance, in terms of number of queries, between the
source of the search and the target is called degrees of
separation. Based on the notion of contacts , we create
logical short cuts to reduce the degrees of separation.
We study the number of needed short cuts and how they
should be distributed across the network.
III. S MALL WORLDS SIMULATION AND ANALYSIS
We start our experiments by investigating several
layouts of wireless networks. Without loss of generality,
we choose a setting of 1000 nodes over a 1kmx1km
area. We investigate various distributions of node
placement, including random, normal, skewed and grid.
Some of the topologies are shown in Figure 1 . Several
values of radio ranges were chosen to provide different
number of links and average node degrees. A subset of
the topologies used in our study is given in Table 1 . Re-wiring experiments were conducted on the
above networks, where a node is chosen at random and
one of its neighbors is chosen at random, then the link
between them is removed and re-linked to a random
node. Because this may result in network disconnection,
which may affect our results, we also performed link

nodes were chosen within a distance d. Path length and clustering exhibited
similar dynamics as d increased.
3 addition experiments, where 2 nodes are chosen at
random and a link is added between them.

(a) 60-random (b) 60-normal
(c) 50-skewed (d) 50-grid
Figure 1 Some topologies used in the study: (a) randomly located nodes with
65m range, (b) nodes located with a normal distribution (avg. 500, std. 250)
with 65m range (c) nodes located with a skewed distribution with 55m range,
(d) nodes located on a grid with 50m range.
Topology Range (m) Links Topology Range(m) Links
55-random 55 4785 35-grid 35 1936
65-random 65 6850 50-grid 50 3811
65-normal 65 10790 75-grid 75 9310
55-skewed 55 10051 100-grid 100 12872
Table 1 Topologies used in our study
Re-wiring and link addition experiments were
conducted for various numbers of links (or probability
of re-wiring/addition). For every probability of re-
wiring or link addition, p, the average path length, L , maximum path length, m, and clustering coefficient, C,
are measured. For the original case, p=0 , (without re-
wiring or link addition) these values are denoted as
L(0) , m(0) and C(0) , respectively. For other values of p we get L(p) , m(p) and C(p) , respectively. We plot the
ratios L(p)/L(0) , m(p)/m(0) , and C(p)/C(0) on a semi-log
plot. These ratios represent reduction in length or
clustering with increased probability of re-wiring or link
addition. Some of the results are shown in Figure 2 . For
all the other experiments we got strikingly similar
results.
0 0.2
0.4
0.6
0.8
1 0.0001 0.001 0.01 0.1 1 p C(p)/C(0)
L(p)/L(0)
m(p)/m(0)
Figure 2 . Reduction of path length and clustering vs. probability of re-linking
We note several observations on these results. First,
the values for clustering and path length of the original
graphs (before re-wiring or adding links) are quite high
as compared to those of random graphs. These values
are shown in Table 2 . One exception is for 35-grid,
where C(0)=0 . Aside from this exception, wireless
networks, in general, tend to be highly clustered (as we
expected) due to the locality of the links, which
increases the probability that a node’s neighbors are
also neighbors of each other.
Rand graph 55-rand Normal Skewed 35-grid 50-grid
C(0) 0.009 0.58 0.568 0.567 0 0.45
L(0) 3.3 12.3 6.9 8.92 21.1 14.8
m(0) 5 31 21 32 62 31
Table 2 Clustering, path length and maximum length for the original
networks without re-wiring or link addition ( D is the network diameter)
Second, from the Figure, we observe a very
consistent trend among all the experiments and across
all topologies. There is a clear distinction between the
reaction of the path length and clustering to re-wiring or
link addition. The path length reduction occurs quite
drastically for 0.2% to 20% of re-wiring. Further re-
wiring does not contribute much to reducing the path
length. We found that on average, re-wiring or addition
of 0.2% of the links results in 25% reduction in L , re-
wiring/addition of 2.58% results in 50% reduction and
re-wiring/addition of 19.8% results in 70% reduction.
Finally, there is a very clear difference between the
path length and clustering dynamics with link re-wiring
or addition. For example, to achieve 75% for L(p)/L(0)
we need around 0.2% re-wiring, but to achieve 75%
C(p)/C(0) we need around 9% re-wiring, i.e., there are
two orders of magnitude difference for the needed re-
wiring. This suggests that by adding or re-wiring a very
small number of links we can drastically reduce the path
length while not affecting the structure of the
4 underlying network. These results seem consistent with
the small world graph phenomenon.
If we consider reduction in clustering as a measure
for the change in the structure of the network, then it
would be interesting to investigate the point of
maximum reduction in path length reduction with
minimum re-structuring of the network. To achieve this,
we define the metric C/L equal to C(p)/C(0)/(L(p)/L(0)) , and the metric C/L/(C/L) max to normalize C/L . In
Figure 1 , we plot this value for the various graphs under
study and the relational graphs (that were studied in [2] ).
It is quite interesting to see the trend of such value with
the probability of re-wiring or link addition, p, as shown
in the Figure. Although the values may not be the same
for all p , the trend is very similar, with the maximum
point around p =3% to 9%. This shows that, up to a
point, significant decrease in path length may be
achieved while maintaining the clustering structure of
the network. Beyond such point minor reduction in path
length requires significant change in the clustering and
hence the structure of the network.
0 0.2
0.4
0.6
0.8
1 0.0001 0.001 0.01 0.1 1 p C/L/(C/L)max Relational
50-ra-rewire
50-ra-add
50-grd-
rewire
Figure 3 Normalized C/L ratio with max around 3%-9%
The previous analysis shows that, for the studied
networks, it seems quite possible to achieve significant
reduction in degrees of separation in wireless networks
by adding a few (say 0.2%-2%) random links. What has
not been clear this far is how random should the
random links be? From a practical point of view,
choosing random contacts for a node in an ad hoc or
sensor network may result in unpredictable overhead to
select and maintain routing for that contact. So the next
step would be to investigate the possibility of limiting
the distance from which a contact may be chosen (such
that the overhead is more predictable), while still
achieving good path length contraction. The next set of
experiments address exactly this issue.
For this set of experiments we add a small number
of links that achieved a large decrease in path length.
We choose three values for the added links: 25, 80, and
150 links (these values achieved between 40-60%
reduction in L in our previous experiments). We want to
obtain the link (or contact) distance that achieves the
largest reduction in L . In these experiments, we limit the
maximum distance (in hops) from which a contact
maybe chosen by a node, call this distance r . A contact
may be chosen at random from a distance d , where
2< d < r . We vary r from 2 to the network diameter D.
Results are shown in Figure 4 . The experiments show a
clear and consistent trend for all topologies
3 . The path
length reduction, L(p)/L(0) seems to increase with the
increase of the distance r up to a certain fraction of
network diameter D , then it saturates . Further increase
in the distance r does not seem to add much to the path
length contraction. We measured the fraction r/D after
which further increase did not affect the reduction by
more than 3%. The average of such fraction for the
topologies studied was around 45% (with minimum of
35% and maximum of 50%).
Since the contact is chosen randomly from [2, r ] hops, we expect the average contact distance, d av
, to be
around 20-35% of the network diameter in order to
achieve the most significant and effective reduction in
path length. Note that the probability distribution is
actually weighted by the number of nodes at each hop,
this turns out to be a bit higher than 2 + [r-2]/2. This
result is further discussed later.
0 0.2
0.4
0.6
0.8
1 0 0.2 0.4 0.6 0.8 1 r/D
L(p)/L(0) 25 links
80 links
150 links
Figure 4 Path length reduction vs. max contact distance r normalized by
network diameter D .
3 The Figure shows results for 55-random. Very similar trends were observed
in the other topologies.
5 0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 0 0.2 0.4 0.6 0.8 1 r/D
L(r)/L(0)
C(r)/C(0)
m(r)/m(0)
Figure 5 Choosing contacts from exactly r hops. Decrease in path length is at
a maximum around 25-40% of the network diameter D.
The next set of experiments involved choosing the
contacts from exactly r hops away and investigating the
trends in path length and clustering. We wanted to see if
we will get consistent results with the previous
experiments. The results are shown in Figure 5 (similar
results obtained for all topologies). To our surprise, the
curve does not saturate after a certain distance. What is
observed is that at a certain distance (roughly between
25-40% of the network diameter) the maximum
reduction in path length is achieved, after which the
path length increases. Perhaps this occurs according to
the node distribution with hops where the contact
reaches the maximum number of nodes around that
certain distance, on average. Nonetheless, this seems to
be a result with very significant practical impact. This
indicates very clearly that by limiting the number of
hops between the added links (or contacts) to just a
fraction of the network diameter (say 25%) we can
achieve maximum reduction in path length or degrees
of separation. This result, along with the previous
observations encouraged us to pursue our contact-based
architecture described in the rest of this document.
Discussion
Previous work done by Kleinberg [4] suggests that,
in a 2-dimensional grid, the best message delivery time
measured in number of forwarding steps (which
corresponds to degrees of separation in our case) is
achieved when the short cuts are chosen with a
probability inversely proportional to their distance from
a node. For example, for two nodes A and B separated
by distance d(A,B) hops, the probability of B being a
contact for A is d(A,B)
-r
, where r is variable. More
specifically, the best performance occurs when r=2 , as
the expected number of forwarding steps is at most
proportional to (log n ) 2 (with each node knowing about
only its neighbors and one contact). Note that in order
to obtain this probability in an ad hoc network each
node needs global knowledge of the locations of all
other nodes in the network (or at least prior knowledge
of the node distribution with hops w.r.t. each node).
This is not practical. However, if this probability is per
hop, a node may identify itself as d hops away from
another node (using TTL or similar), and can compute
this probability independently with a rough estimate of
the network diameter, D , in a decentralized way.
So, what we want to study is the distance (in hops)
that achieves the best performance. Note that d -2
used
in [4] is per node (not per hop). We want to obtain the
expected number of hops for such probability
distribution. Given the 2-dimentional grid and given a
general node near the center of the grid, the number of
nodes that can be reached at exactly d hops away is 4 d (approximate for the regular grid and exact for the grid
on a sphere). Taking the probability of each node to be
1/d
2 and that 4 d nodes are at hop d we get the hop
probability distribution as 1/d (i.e., the probability of
choosing the contact at hop h is 1/ h ). To get the
probability distribution we normalize by Σ 1/d , for all
hops up to the network diameter. Hence the expected
hop value is D/( Σ 1/d)=D/ H(D) , where D is the network
diameter, and Σ 1/d is the harmonic series, H(D) . H(D)= ln(D)+O(1). Around 30-70 hops the ratio ranges
from around 20-25% of D , consistent with our results
above. We also conducted simulations to get the per-
hop distribution and obtained the expected number of
hops for the various topologies under study with an
overall average of 25.5% of D (min 21%, max 34%)
[very much in lines with our results above.].
Next, we attempt to make use of these results to
design a novel contact-based architecture for resource
discovery in large scale ad hoc and sensor networks.
IV. S MALL WORLDS & RESOURCE DISCOVERY IN LARGE-
SCALE WIRELESS NETWORKS
Now that the relationship between small worlds and
wireless networks has been established, we need to ask
the question ‘How do we make use of such information
to design better architectures and protocols for ad hoc
and sensor networks?’ First, now we have a good
estimate of the number of short cuts to be established in
order to achieve significant path length reduction. We
also have a good estimate of the distance of these links.
So, how can we establish those links in wireless
networks? and what do they mean? We shall address the
latter question first. Short cut links in relational graphs
may be obtained practically by adding a physical (wired
or other) link between the chosen nodes. In ad hoc
6 networks, however, the physical constraint posed by the
transmission range renders the ad hoc network a ‘spatial
graph’, which cannot include random links naturally.
Note that short cuts may be achieved by increasing the
transmission range to establish the link. This however,
may also be limited in distance , causes increased power
consumption, and has negative effects on utilization of
the spectrum. Some systems may exploit several radios,
one with short range (and high data rate) and another
with longer range (and low data rate), which may
establish the short cut. This may be a possible system to
investigate in the future. In this study, however, we do
not assume that such capability exists and hence our
short cut (for the remainder of this document) will be a
logical link that will translate into several physical hops.
The logical link, in our case, corresponds to one degree
of logical separation.
Thus, our goal is not to reduce the physical path
length. Rather, we aim to reduce the logical path length
(in terms of degrees of separation) and in turn reduce
the number of queries during resource discovery. This,
along with the insights gained from our experiments
(such as the number and placement of contacts)
establishes a clear link between the previous part of the
paper on small worlds and the coming part on resource
discovery in ad hoc and sensor networks.
Also, note that the above analysis, for L ,C and m , showed the existence (and context) of the small world
characteristic, using short cuts, in wireless networks. It
did not show, however, ‘how to find and use those short
cuts’. This question is only answered through
architectural and protocol design; a subject we shall
discuss for the remainder of this paper.
V. R ELATED WORK ON RESOURCE DISCOVERY IN
WIRELESS NETWORKS
We address the problem of resource discovery in
infrastructure-less networks. The resource discovered
may even be a route. Hence, architectures that require
infrastructure (e.g., DNS) or that assume existence of
underlying routing are not suitable for our problem.
Centralized approaches are neither robust nor scalable.
In wireless ad hoc and sensor networks perhaps the
simplest form of resource discovery is global flooding.
This scheme does not scale well. It also uses broadcast,
which is usually unreliable at the data link layer (e.g., in
802.11). The synchronization of the broadcasts may
lead to severe collisions and medium contention. Hence,
it is our design goal to avoid global flooding.
Expanding ring search uses repeated flooding with
incremental TTL. This approach also does not scale
well. Much of the work on routing protocols in ad hoc
networks uses some form of flooding or ring search
(e.g., DSR [7] , AODV [6] , DSDV [5] , ODMRP [8] ).
Other approaches in ad hoc networks that address
scalability employ hierarchical schemes based on
clusters or landmarks (e.g., LANMAR [10] and [9] ).
These architectures, however, require complex
coordination between nodes, and are susceptible to
major re-configuration (e.g., adoption, re-election
schemes) due to mobility or failure of the cluster-head
or landmark. Furthermore, usually the cluster-head
becomes a bottleneck. Hence, in general we avoid the
use of complex coordination schemes for hierarchy
formation, and we avoid using cluster-heads.
In GLS [11] an architecture is presented that is
based on a grid map of the network (that all nodes know
of). Nodes recruit location servers to maintain their
location. Nodes update their location using an ID-based
algorithm. Nodes looking for location of a specific ID
use the same algorithm to reach a location server with
updated information. This is a useful architecture when
a node knows the network grid map, knows its own
location (through GPS or other), and knows the ID of
the node it wishes to contact. These assumptions may
not hold in our case. Especially that a source node has
to know the specific ID of the target node and uses that
ID to locate the traget’s location servers. By contrast, in
our architecture, a source node may be looking for a
target resource residing at a node with an ID unknown
to the source node.
The algorithm proposed in [4] and [12] uses global
information about node locations to establish short cuts
or friends, and uses geographic routing to reach the
destination. It is unclear how such architecture is
feasible with mobility. Also, such work does not specify
the number of short cuts to create. In addition, the
destination ID (and location) must be known in
advance, which may not be the case in resource
discovery.
In ZRP [13] the concept of hybrid routing is used,
where table-driven routing is used intra-zone and on-
demand routing is used inter-zone. Border-casting
(flooding between borders) is used to discover inter-
zone routes, which may not scale well. A good feature
in ZRP is that a zone is node-specific. Hence, there is
no complex coordination susceptible to mobility as in
cluster-head approaches. We use the concept of zone in
our architecture. However, we avoid border-casting by
using contacts out-of-zone.
In [14] an architecture based on intelligent agents is
introduced for resource discovery in ad hoc networks.
7 The concept of domains is used and a cluster-head
election is needed to define a domain.
VI. CONTACT-BASED ARCHITECTURE
First, we state the assumptions upon which our
architecture is built.
Assumptions: (1) The source does not know the ID of
the target node that holds the resource. (2) Nodes only
have local knowledge of their neighbors (e.g., using 1
hop Hello or data link connectivity). (3) Nodes do not
know their own location or any other geographical
location of any other node (i.e., our architecture does
not require GPS or any other GPS-less distance
estimation techniques)
4 . (4) Infrastructure-less network:
We assume there are no well-known servers or
landmarks. (5) We assume rough knowledge of network
size (number of nodes) at the design stage.
These assumptions differentiate our work from other
works that require any of the above elements.
Architecture: We propose what we call a loosely
coupled simple hierarchy. It is loosely coupled because
each node has its own view of the network (its zone),
and it is simple because there are no complex
coordination mechanisms to elect cluster-heads or
leaders. In our architecture, each node knows a number
of neighboring nodes in a neighborhood or zone. The
zone may be defined , for example, by a number of hops
R . Routes to nodes within the zone are established by a
local table-driven intra-zone routing protocol (e.g.,
DSDV). Outside of the zone, a node may maintain (a
small number of) contacts. A contact is chosen at r hops
distance from the selecting node. The contact may be
maintained up to r max hops away. We presented a very
high level sketch of this idea in [15] without details.
The idea behind the contacts stems from the small
world concept, but also for increased coverage and
reachability of other nodes. A contact outside a node’s
zone will also have its own zone, thus providing an
extended view of the network.
The idea behind our architecture is simple.
However, several challenging questions impose
themselves. What should be the value of the zone
radius, R ? What should be the contact distances r and
r max
? How many contacts should be established? How
will the query mechanism be implemented on top of
such architecture? And, perhaps one of the most
important issues, how will these contacts be chosen and

4 Availability of such location information may simplify our architecture.
Studying such simplifications is part of on-going and future work.
how will mobility affect this architecture? We leave this
latter question for detailed treatment in the next section.
To answer the first few questions about R , r , contact
number ( CN ) and the query, we perform an evaluation
of the design space. Also, we define new parameters for
the query, the query depth, QD , and the contact level.
For a node, its contacts are level-1 contacts. Then its
contacts’ contacts are level-2 contacts, so on. The
contact depth is the number of levels of contacts that the
query is allowed to reach, in order to search for the
target. For example, a scheme in which a node queries
only its contacts for the target is a QD=1 scheme.
For brevity, we show our analysis of the 55-Rand
topology shown earlier. Similar analysis may be
performed for other topologies as well.
Simulations were run for 1250 queries (from 25 random
sources, each to 50 random targets), and were averaged
for different random seeds. Figure 6 , shows the un-
reachability (i.e., the % ge of failed searches for a
target), as function of R and the query depth. Our
findings show that the parameter that affects
reachability the most is the query depth. This is because
the number of contacts searched grows exponentially
with QD. Also, R has significant effect on reachability.
As R is increased, the number of nodes reached in-zone
grows significantly. For r it turns out that so long as r is
around 2R or greater, reachability does not change
drastically. The reason for this is at r > 2R we get no
overlap between the source’s zone and the contact’s
zone.
We also need to consider overhead of changing R , QD and r . The greater these values, the greater the
overhead of intra-zone routing, querying and contact
maintenance, respectively. So, we choose min values
that achieve very good reachability. From our results we
pick R=4, QD=4, r=7 (this also coincides with our
small world finding as 22% of D (31)) . 1 2 3 4 5 6 1 3 0 20
40
60
80
100
query depth ' D '
( r = 7)
R (hops)
%ge unreachability 2 4 Figure 6 Reachability as function of zone radius and query depth.
8 For the number of contacts CN per node (not shown for
brevity), the effect on reachability is nearly linear.
However, we do not recommend to increase the number
of contacts per node. Rather, we should introduce the
notion of contact sharing among nearby nodes. This
reduces the overhead of contact selection and
maintenance. Issues of contact sharing are part of on-
going and future work. For now, we may intuitively
recommend between 80-150 contacts for the whole
topology (these were numbers that achieved very good
path length reduction in our small world analysis). We
shall also investigate a lazy (or on-demand) approach
for contact selection in the future. We shall also
research the generality of our findings to other topology
configurations (with varying number of nodes and
transmission ranges), and investigate scaling factors
that easily translate these results from one topology to
another. Another future issue is dynamically
configuring these parameters. In this study we address
parameters setting at the design stage, assuming that the
rough network size is known. In the next section we
address the issue of contact selection.
VII. M OBILITY-BASED CONTACT SELECTION PROTOCOLS
One of the main challenges that we need to address in
our architecture is the effect of mobility and its
dynamics on contacts. We pose this challenge in the
form of the following question. How will contacts be
selected with reasonable overhead, while achieving the
small world characteristics under mobility conditions?
To attempt to answer this question we first address the
question of contact selection and present various
protocols that address mobility issues. Then we evaluate
the effect of mobility on selected contacts. Our goal in
this study is to gain better understanding of the interplay
between contacts and mobility.
A. Contact Selection
As was pointed out earlier, according to our
analysis a desirable region for a contact to be in (for our
studied topologies and those similar) is around 20%-
25% of the network diameter, D . How can a node select
a contact so many hops away with reasonable overhead
(without resorting to global flooding)? At the same
time, we want the selection process to elect contacts
that are also likely to remain in the desirable region
long enough to be useful in resource discovery. How
can the selecting node choose the contacts intelligently,
given that the desirable region will be out-of-zone . This
problem is challenging for two main reasons. First,
mobility seems as an adversary, providing random
movement and contributing to link and path failure.
Second, the selecting node is likely to know little or no
information about the mobility characteristics and
capabilities of nodes in the desirable region.
Border Node
Center Node
Internal Node
Mobility
R S 5 1 4 3 6 7 2 Zone Radius
Route
R R R R S 5 1 4 3 6 7 2 contact
contact
contact
(a) ( b)
R R R R S 5 1 4 3 6 7 2 contact
contact
( c)
Figure 7 Example of zoning, contacts and effect of mobility: (a) Zone for
source node S is shown (with radius R ). Border nodes are numbered (1-7).
Nodes 1,3 and 6 are moving/drifting out of zone. (b) Radii for the drifting
nodes are shown. S stays in contact with the drifting nodes, which enables it
to obtain better network coverage with low overhead. (c) After moving away,
contact nodes drift up to a point where their zones no longer intersect with
S ’s zone. In this example, S maintains contact with those nodes not more
than (2 R +1) hops away, i.e. nodes 3 and 6, and loses contact with node 1 as it
drifts farther than the contact zone.
Our proposed answer to the above question is to
take advantage of mobility using a novel approach
called mobility-based contact selection. In our
approach, a selecting node, S, makes initial selection of
a list of candidate contacts ( CCs) from its own zone.
These are nodes that lie within R hops away. S knows
routes to these nodes via intra-zone routing. This way, S may also collect information about CCs’ mobility or
abilities. This information may be piggybacked over the
intra-zone route exchange. The future contacts are to be
chosen from this list of CCs. Once these candidate
contacts move out-of-zone, overlap between their zones
and S’s zone will be reduced and the added network
view (or coverage) will be significant, as shown in
Figure 7 . Still, some questions remain regarding the
dynamics of these contacts. Will they move into the
9 desirable region and for how long? How long will they
remain candidates before they do enter the desirable
region? To get a better understanding of the effect of
mobility on our proposed approach, we define two
different protocols for mobility based contact selection.
Let us start by defining the overall scheme of
contact selection , then move into the details of the
individual protocols. In both protocols, a node, S, starts
selecting a list of candidate contacts ( CCs) from the
zone (i.e., within R hops). Based on its mobility pattern,
a node on the CCs list may get promoted to contact or
get dropped (or evicted) from the candidacy list based
on promotion/eviction rules. By mobility pattern we
mean the sequence of distances (in hops) between these
candidates and the selecting node, over time. The
protocols differ in the way they select candidates from
the zone, and the way they use the mobility pattern in
conjunction with the promotion/eviction rules.
R S Z A B C
R R S Z contact
A B C (a) ( b)
Figure 8 The zone information propagation ( ZIP ) local route
discovery protocol (a) Z is at the border of S ’s zone with a route ‘ S-
A-B-Z’. Z is moving out-of-zone. (b) Z is no longer within S’ s zone,
but it highly likely to exist in B’ s zone. The route ‘S-A-B-C-Z’ is
identified and Z is selected as a contact.
As these CCs move, S keeps track of their distance
(in hops) through intra-zone routing, and when they
move out-of-zone a lightweight local route discovery
mechanism, called zone information propagation ( ZIP ) is used (see Figure 8 ) . When and if a candidate crosses
the promotion boundary (PB) it is considered a contact
and may be queried during searches. Once a contact
crosses the upper or lower eviction boundaries (UEB,
LEB) it is evicted from the contact list and is not
queried in further searches (see Figure 9 ). That is, if a
node moves too far away (beyond the eviction
boundary) it is harder to maintain, whereas if it comes
closer to S its new zone may overlap with that of S, and
is evicted in both cases.
The two selection protocols are called border-based
and neighbor prediction-based contact selection
protocols . S Lower Eviction Boundary
(LEB)
Upper Eviction Boundary (UEB)
Promotion Boundary (PB)
Contact
Evicted
A t1
A t2
A t4
A t3
B t1
Contact
B t2
B t4
Evicted
Figure 9 Promotion and Eviction boundaries for S: nodes A and B originally
in S’ s zone, get promoted at time t2 when they cross the promotion boundary
(PB), then they get evicted from the contact list at time t4 when they cross
the lower or upper eviction boundary.
Border based contact selection protocol: Selection
of candidate contacts is done from nodes at R hops, i.e.,
at the border of the zone. Nodes R hops away are
tracked, i.e. , S keeps track of its movement/distance
over time. If border nodes move closer to S , they are
evicted. If they cross the promotion boundary, those
candidates become contacts. When the contacts cross an
eviction boundary they are evicted.
Neighbor prediction based contact selection
protocol: This protocol takes advantage of the fact that
S readily knows the routes/hop distance to nodes within
its zone (i.e., within R hops away). It also takes
advantage of the likelihood that (even in random way
point movement) mobility often remains constant for
short whiles. In this protocol, node S selects neighbors
(those nodes that are 1 hop away) to track their
movement. When a neighbor node becomes at 2 hops
away, then 3 hops away, this sequence may indicate that
this neighbor is heading out of zone and has a high
probability to continue moving until it becomes in the
desirable region (the probability of this happening is a
function of the mobility pattern and is part of this
study). Other neighbors, that do not show this
consistency in mobility, may take longer (if ever) to get
to the desirable region and thus waste more resources
before becoming useful, and so are evicted from the
CCs list. We expect this simple prediction scheme to
help identify good candidates that have higher
probability of becoming contacts. We plan to
investigate such behavior in our simulations and
analysis.
10 B. Evaluation under mobility
First, we define our evaluation metrics based on our
study questions. We define the contact persistence , as
the life span of a contact (the point in time when the
candidate contact became a contact until the time it was
evicted). In general, the more the persistence the better,
since we want the contact to remain in the desirable
region for a longer time and be useful for more queries.
The second metric we define is the average overlap
range . For each source node choosing contacts, this
metric measures, at each instance in time, the pair-wise
zone overlap distance of its contacts, normalized by the
number of pairs (say if we have n contacts, then n(n-
1)/2 is the normalization factor). This is averaged for all
the sources in the simulation run. It may also be
averaged over the simulated time to get the average of
the averages. This metric attempts to capture the
coverage overlap between the contacts. The less the
better. Another metric is the expected time for a node to
become a contact (the faster the better). Yet others
include the number of contacts (or % ge of CCs list
becoming contacts), number of contacts evicted by the
upper boundary vs. lower boundary (the more at the
upper boundary the better, than means they went
through the desirable region), among others.
For mobility we use the random way point model,
in which a node chooses a random destination and picks
a random velocity from [0,Vmax]. Once the destination
is reached another destination and velocity are picked,
so on. We use a pause time of 0, i.e., continuous
mobility.
We investigate several dimensions in the design
parameter space. For both protocols, we vary the
promotion and eviction boundaries systematically and
observe the change in the above metrics. We vary the
number of neighbors/borders chosen initially by each
protocol. We also vary the max velocity used. For
brevity we only show results for one topology, 1000
node, 1kmx1km, 55-Rand described earlier (similar
analysis maybe carried out similarly for other
topologies). We use R=4. Note that r now is a function
of the promotion and eviction boundaries. We vary the
promotion boundary (PB) and the lower and upper
eviction boundaries (LEB, UEB), sometimes allowing
hysteresis (i.e., PB > LEB). PB and LEB are varied
between 4 and 7 and UEB is varied between 10 and 13
(this is the space of parameters we were most interested
in analyzing based on our previous analyses).
The simulations were run for 100 and 200 seconds,
with Vmax ranging from 1m/s to 40m/s, using 50
randomly selected sources ( S) , tracking 7, 14, 20
borders each (for the first protocol) and all 1
st
hop
neighbors (for the second protocol). We discuss a subset
of our results showing the most interesting trends.
0 5 10
15
20
25
30
35
1m/s 2m/s 10m/s 20m/s 30m/s 40m/s
Contact distance distribution with velocity [Vmax] (tracking
neighbors)
%ge time spent at that distance for 200 simulated seconds (a) tracking neighbors
0 5 10
15
20
25
30
35
40
45
1m/s 2m/s 10m/s 20m/s 30m/s 40m/s
Contact distance distribution with velocity (Vmax) [R=3, border
based selection]
%ge time spent at that distance for 200 simulated seconds (b) tracking borders
Figure 10 Tracking experiments
To get a feel of the node movement, especially the
relative distance (in hops) between a selecting source
node ( S) and a tracked node (candidate contact or
contact), we present a set of tracking experiments
without boundaries. Since the two protocols track
different nodes (the first tracks border nodes and the
second tracks 1
st
hop neighbors) we conduct both
experiments. As shown in Figure 10 (a) and (b), the
eventual distribution of relative distances seems to be
quite similar for both protocols and it saturate around
20m/s and above. The graphs show that, in general, the
nodes spend much of their time between 4 and 9 hops
away from their corresponding S . The distribution is
very similar to that of the node-spread distribution (or
node-hop distribution) for that topology. This seems
promising because of the reasonable probability that a
tracked node will spend time in the desirable region.
Also, we notice that, over time, for the tracked borders
much time is spent in hops closer to S than the border
11 (i.e., hops 1, 2). This may indicate a notable probability
of border nodes moving closer to S before moving out-
of-zone. We shall investigate this effect further as part
of the experiments below. The graphs do not show,
however, the movement pattern for individual nodes.
Such pattern is captured in the next set of experiments.
We now study the effect of varying the promotion
boundary (PB) and the lower eviction boundary (LEB).
As shown in Figure 11 , (for the neighbor prediction
protocol and 20m/s Vmax), the number of contacts
selected increases with the decrease in PB. Also, the
number of remaining contacts decreases with the
increase in LEB. Contact persistence drops from an
average of 42.9sec (PB=4,LEB=4) to 27.15sec
(PB=7,LEB=4) to 18.5sec (PB=7,LEB=7). On the other
hand, the average overlap range was as follows: 23.2m
(PB=4,LEB=4), 15.9m (PB=7,LEB=4), 12.5m
(PB=7,LEB=7). We notice that overlap increases with
number of contacts and with lowering PB. With
decreased PB the contacts will be relatively closer to S and hence have higher probability of being close to each
other as well. With increase in LEB we expected to see
a significant drop in overlap. However, the drop was
minor. This indicates that most contacts crossing PB
moved to farther relative distances. To follow up on this
observation we look at the number of contacts evicted at
LEB vs. those evicted at UEB. Recall that being evicted
at UEB is preferable because the contact will have
crossed the whole desirable region. The numbers were
as follows (for the same overall number of selected
contacts, 301 contacts): LEB=4 achieved 50 LEB
evictions and 235 UEB evictions (16 contacts remained
at the end of simulation), whereas LEB=7 achieved 83
LEB evictions and 210 UEB evictions (8 contacts
remained). Hence all the extra evictions due to lowering
LEB seem to have been for useful contacts (that would
have otherwise crossed over to UEB and been UEB
evictions, or remained as contacts). Hence, allowing
the contacts (elected at 7 hops) to remain contacts
between 4-7 hops, gives them a highly probable
opportunity to move on to the desirable 7-10 hops
region without crossing the 4 hops boundary. This
argues in favor of the ‘ hysteresis’ scheme
(PB=7,LEB=4). From the above analysis we
recommend a setting of (PB=7,LEB=4).
0 50
100
150
200
250
1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196
time (sec) [UEB=10]
Number of Contacts PB=4,LEB=4
PB=7,LEB=4
PB=7,LEB=7
0 10
20
30
40
50
60
70
80
90
1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196
time (sec) [UEB=10]
Average Overlap Range Figure 11 Effect of varying the promotion boundary (PB) and the lower
eviction boundary (LEB) for the neighbor prediction protocl.
Next we study the effect of changing the upper
eviction boundary (UEB). As shown in Figure 12 , the
number of remaining contacts increases with the
increase in UEB, and so does the average number of
contacts over time. In addition, contact persistence
increases from 27.15sec (UEB=10) to 36.5 (UEB=11)
to 42.19 sec (UEB=12) to 49.53 (UEB=13). We also
notice an increase in average overlap with increase in
UEB, from 15.9m (UEB=10) to 18.9 (UEB=11) to 21.6
(UEB=12) to 23.97 (UEB=13). (Remember that the
zone radius is R =4 and the transmission range is 55m).
This increase is probably partially due to increase in
average number of contacts. It may also be due to the
fact that after a specific number of hops, contacts tend
to cluster near the boundary of the network, which
reduces their relative distances. The increase does not
seem significant though. Hence, it seems from this
analysis that the higher UEB the better. What is missing
from this data, however, is the change in maintenance
overhead with increased UEB. This needs more detailed
description of the protocol and is part of our future
work.
Next, we compare the performance of the two
different contact selection protocols. We discuss our
results for PB=7, LEB=4, UEB=10, Vmax=20m/s, and
12 300 selected contacts
5 . For the boundary-based
selection we notice that the expected time for contact
promotion (10.25sec) is much lower than that in the
neighbor prediction scheme (45 .18 sec). We also notice
that a much larger % ge of tracked nodes that converted
into contacts was much higher in the neighbor
prediction scheme (80%) than in the border selection
scheme (54%). This is due to the filtering scheme that
occurs during prediction, where nodes not conforming
to the prediction rule are not tracked at the boundary of
the zone. Average overlap was very similar in both
cases. Contact persistence, however, was much higher
in border selection (45.8sec) than in neighbor prediction
(27.15sec). This could be due to the faster promotion in
the former scheme. Hence, if the border tracking can be
achieved without more overhead than neighbor tracking
then it seems that border selection scheme is better.
Tracking overhead analysis is part of our future work.
0 20
40
60
80
100
120
140
160
180
1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196
time (sec) [PB=7,LEB=4]
Number of Contacts UEB=13
UEB=12
UEB=11
UEB=10
0 10
20
30
40
50
60
1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196
time (sec) [PB=7,LEB=4]
Average Overlap Region Figure 12 Effects of varying the eviction upper boundary (UEB)
VIII. C ONCLUSIONS AND FUTURE WORK
We have established a relationship between small
world graphs and wireless ad hoc and sensor networks.
Our findings indicate that by adding a few short cuts,
with only a small fraction (~20%) of the network
diameter, the degrees of separation may be reduced

5 This provides a fairer comparison since the number of selected contacts
depends on the number of candidates (for first protocol may be much more
than 1
st
hop neighbors).
drastically. This was established both through extensive
simulations and through analysis. Based on this finding
we proposed a novel contact-based architecture for
resource discovery in ad hoc and sensor networks. To
realize such architecture efficiently, we introduced a
new class of protocols called mobility-based contact
selection protocols, including two selection protocols,
local route discovery protocol and a set of
promotion/eviction rules. Our experiments on contact
selection protocols and node tracking enabled us to
develop a base-line understanding of the mobility
dynamics and its effect on our architecture. Initial
results indicate promise of the proposed schemes, and
point to favorable parameter settings for our protocols.
Future study is needed to further enhance our
understanding and investigate more traditional metrics
for evaluation (such as coverage and overhead). We
plan more detailed evaluation of our schemes using
various mobility models (e.g., group mobility, freeway
models, etc.). We also plan to investigate other
heuristics for contact selection based on minimum
overlap rules.
R EFERERNCES
[1] S. Milgram, “The small world problem”, Psychology Today 1, 61
(1967)
[2] D. J. Watts. In Small Worlds, The dynamics of networks between order
and randomnes s. Princeton University Press, 1999.
[3] D. Watts, S. Strogatz, “Collective dynamics of ‘small-world’
networks”, Nature 393, 440 (1998).
[4] J. Kleinberg, “Navigating in a small world”, Nature, 406, Aug. 2000.
[5] C. E. Perkins, P. Bhagwat, Highly Dynamic Destination-Sequenced
Distance Vector Routing (DSDV) for Mobile Computers, Comp.
Commun. Rev., Oct. 1994, pp. 234-44.
[6] C. E. Perkins, E. M. Royer, Ad-hoc On-Demand Distance Vector
Routing, Proc. 2
nd IEEE Wksp. Mobile Comp. Sys. And Apps ., Feb.
1999, pp. 90-100.
[7] D. B. Johnson, D. A. Maltz, Dynamic Source Routing in Ad-Hoc
Wireless Networks, Mobile Computing, 1996, pp.153-181.
[8] S. Lee, M. Gerla, C. Chiang, “On-demand multicast routing protocol”,
IEEE WCNC, p. 1298-1302, vol. 3, 1999.
[9] B. Das, V. Bharaghavan, “Routing in ad-hoc networks using minimum
connected dominating sets”, in Proc. IEEE ICC ’97.
[10] P. Guangyu, M. Gerla, X. Hong, “LANMAR: landmark routing for
large scale wireless ad hoc networks with group mobility”, MobiHOC
’00, p. 11-18, 2000.
[11] J. Li, J. Jannotti, D. Couto, D. Karger, R. Morris, "A Scalable Location
Service for Geographic Ad Hoc Routing", ACM Mobicom 2000.
[12] L. Blazevic, S. Giordano, J .-Y. Le Boudec “ Anchored Path Discovery
in Terminode Routing”. Proceedings of the Second IFIP-TC6
Networking Conference (Networking 2002), Pisa, May 2002.
[13] M. Pearlman, Z. Haas, “Determining the optimal configuration for the
zone routing protocol”, IEEE JSAC, p. 1395-1414, vol. 17, 8, Aug
1999.
[14] J. Liu, Q. Zhang, W. Zhu, J. Zhang, B. Li, “A Novel Framework for
QoS-Aware Resource Discovery in Mobile Ad Hoc Networks”, IEEE
ICC ’02.
[15] A. Helmy, "Architectural Framework for Large-Scale Multicast in
Mobile Ad Hoc Networks", IEEE ICC ’02.

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Description

Ahmed Helmy. "Small large-scale wireless networks: Mobility-assisted resource discovery." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 770 (2002).

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Core Title USC Computer Science Technical Reports, no. 770 (2002)

Alternative Title Small large-scale wireless networks: Mobility-assisted resource discovery (title)

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