Computer Science Technical Report Archive

USC Computer Science Technical Reports, no. 886 (2006)

(USC DC Other)

USC Computer Science Technical Reports, no. 886 (2006)

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content Nearest Neighbor Queries with Data Sharing in Mobile Environments Wei-Shinn Ku, Roger Zimmermann, and Chi-Ngai Wan Computer Science Department University of Southern California Los Angeles, California 90089. USA [wku,rzimmerm,cwan]@usc.edu Abstract Mobile clients feature increasingly sophisticated wireless networking support that enables real-time information ex- change with remote databases. Location-dependent queries, such as determining the proximity of stationary objects (e.g., restaurants and gas stations) are an important class of in- quiries. We present a novel approach to support nearest- neighbor queries from mobile hosts by leveraging the shar- ing capabilities of wireless ad-hoc networks. We illustrate how previous query results cached in the local storage of neighboring mobile peers can be leveraged to either fully or partially compute and verify spatial queries at a local host. The feasibility and appeal of our technique is illus- trated through extensive simulation results that indicate a considerable reduction of the query load on the remote data- base. Furthermore, the scalability of our approach is excel- lent because a higher density of mobile hosts increases its effectiveness. 1 Introduction Location-based queries are of interest in a growing num- ber of applications and an important sub-class of such queries are nearest neighbor (NN) searches. Increasingly such queries are issued from mobile clients and there exist several algorithms that allow the efficient execution of NN queries on centralized databases. In this study we propose an approach that leverages short-range, ad-hoc networks to share information in a peer-to-peer (P2P) manner among mobile clients to answer location-based nearest neighbor queries. Such a P2P approach can be very valuable for appli- cations where access to the server is not always guaranteed and may be spurious at times. For example, during a natural disaster such as an earthquake or a hurricane, the commu- nication from rescue crews to stationary databases may be intermittent. In such a scenario, P2P data sharing can pro- vide a robust alternative where fault-resilience is naturally built into the design. 1NN Candidates 1NN 1NN Communication range q p 1 p1 p 2 p2 n1 n2 n3 n4 Figure 1. Nearest neighbor peer-to-peer result shar- ing. The efficiency of our approach is derived from the obser- vation that the results of spatial queries often exhibit spa- tial locality. For example, if two mobile hosts are close to each other, the result sets of their kNN queries for a spe- cific object type may overlap significantly. Through mobile cooperative caching of the result sets, query results can be efficiently shared among mobile clients [3]. Figure 1 shows an example. At time T the mobile query point q can establish contact with two other mobile hosts within its communication range: p 1 and p 2 . Both of these clients in the past executed a 1NN query for the nearest fire station when they were located at p 1 and p 2 , respectively 1 . The results that they obtained and cached weren 2 ,p 1 and n 4 ,p 2 . These two tuples represent candidate solutions for q’s own 1NN query. Through a local verification process q can determine whether one of the solutions obtained from its neighbors is indeed its own nearest fire station. Note that the current location of the neighboring hosts, p 1 and p 2 , has no specific significance, as long as they are within q’s com- munication range. The contributions of this study are as follows. We first identify a set of characteristics that enable the development 1 In our notation we use the object identifier to represent its position coordinates. 1 of effective sharing methods. We then introduce a set of al- gorithms that aid in the decision process within this distrib- uted environment to verify whether the data items received from neighboring clients provide a complete, partial, or ir- relevant answer to the posed query. Our initial method ver- ifies results from a single neighbor, and we then extend it to work with multiple neighboring clients. Finally, through extensive simulation experiments we explore the benefits of our approach under different parameter sets (e.g., changes in the mobile host density and the wireless transmission range). The rest of this paper is organized as follows. Section 2 surveys the related work for processing kNN queries. Our own approach is detailed in Section 3 and the experimental results are presented in Section 4. Finally, Section 5 con- cludes the paper and outlines future research directions. 2 Related Work The existing work relevant to our approach can broadly be classified into nearest neighbor query processing and cache management in mobile environments. 2.1 Nearest Neighbor Query Processing R-trees [8] and their derivatives have been a prevalent method to index spatial data and increase query perfor- mance. To find nearest neighbors, branch-and-bound algo- rithms have been designed that search an R-tree in either a depth-first [11] or best-first manner [9]. Both types of algorithms were designed for stationary objects and query points. With the emergence of mobile devices attention has fo- cused on the problem of continuously finding k nearest neighbors for moving query points (k-NNMP). A na¨ ıve ap- proach might be to continuously issue kNN queries along the route of a moving object. This solution results in re- peated server accesses and nearest neighbor computations and is therefore inefficient. One method to reduce the com- putational complexity is to sample the trajectory instead of treating it as a continuous curve [12]. 2.2 Cache Management in Mobile Environ- ments Caching is a key technique to improve data retrieval per- formance in widely distributed environments. Leveraging the combined resources of several cooperating caches has been proposed to improve file system [5] and Web perfor- mance [13]. In conventional mobile environments, wireless connections are treated as extensions of the wired infrastruc- ture. Hence, mobile clients retrieve information from data- base servers via intermediate base-stations. With the in- creasing deployment of new peer-to-peer wireless commu- nication technologies (e.g., IEEE 802.11x and Bluetooth) there exists a new information sharing alternative known as peer-to-peer cooperative caching. With this technique mo- bile hosts communicate with neighboring peers in an ad-hoc manner to share information rather than having to rely on the communication link to the remote information sources. Peer-to-peer cooperative caching can bring about several distinctive benefits to a mobile system: improving access latency, reducing server workload and alleviating point-to- point channel congestion. As a disadvantage, it may in- crease the communication overheads among mobile hosts. Recently, a number of techniques have been proposed to ad- dress caching in ad-hoc peer-to-peer networks. The COop- erative CAching (COCA) [3] scheme investigates the effects of client activity levels, data replication, and cache size. The benefits of clustering mobile clients into groups are investi- gated in [4]. While there has been significant prior work in the above two areas, none of the existing techniques encompasses all the features of our proposed approach. 3 System Design The fundamental idea behind our methodology is to leverage the cached results from prior queries at reachable mobile hosts for answering nearest neighbor queries at the local host. To achieve scalability it is imperative that a mo- bile client can locally determine whether the result set from its neighbors provides a full, partial or no answer. As a novel component in our methodology we present a verification algorithm that can validate whether a given re- sult object is part of the solution set. We term such an object verified. If the object is not guaranteed to be part of the result set, we call it unverified. The first variant of our verification procedure validates object certainty from a single peer. We then extend the process to multiple peers. If no full set of verified objects can be retrieved from neighboring peers, the query is forwarded to a spatial database server including the acquired partial result. The database search efficiency can be improved by utilizing the partial query results from peers. In this study we detail how k-nearest neighbor (kNN) queries can be processed by cooperating mobile hosts. In Section 3.1 we introduce the infrastructure that we assume for our work. Next, Section 3.2 presents a three-phase al- gorithm for verifying query results from neighboring peers and explains how to use partial peer results to decrease the server load for processing kNN queries. 3.1 Assumed Infrastructure We are considering mobile clients, such as cars, that are instrumented with a global positioning system (GPS) for continuous position information. Furthermore, we assume that two-tiers of wireless connections are available on future Symbol Meaning P A set of all the peers which respond the query issued by q p.N The most recent query result set of a mobile host p where p∈ P p.R The verified region of a mobile host p q A query mobile host ||a, b|| The Euclidean distance between objects a and b ni A nearest neighbor element in p.N H A heap for storing SBNN query results. Its verified and unverified elements are defined as H.verified and H.unverified, respectively. |A| The number of elements in set A Table 1. Symbolic notations. automobiles. Traditional, cellular-based networks (such as utilized by the OnStar service) allow medium range con- nections to base-stations that interface with the wired In- ternet infrastructure. They usually charge a subscription or metered usage fee. A second type of short-range net- works allow ad-hoc connections with neighboring mobile clients. Technologies that enable short range communica- tion include, for example, IEEE 802.11x using unlicensend, free spectrum. Benefiting from the power capacities of ve- hicles, we assume that each mobile host has a significant transmission range and virtually unlimited lifetime. The ar- chitecture can also support hand-held mobile devices. How- ever, then power consumption becomes an additional para- meter which we are not currently considering. 3.2 Sharing Based Nearest Neighbor Queries With the system infrastructure described in Section 3.1, a mobile host q can collect NN data from peers to harvest these existing results for completing its own Euclidean dis- tance kNN search. We term this approach a Sharing Based Nearest Neighbor (SBNN) query. We propose two approaches to process NN informa- tion obtained from peers. The single peer NN verification process, also called kNN single , attempts to verify the va- lidity of k objects by sequentially verifying results obtained from each single peer. If the number of verified objects is less than k, then the multiple peer NN verification process, kNN multiple , attempts to complete the verification process with several peers simultaneously. Table 1 summarizes the symbolic notations used throughout this section. 3.2.1 Step 1: Single Peer NN Verification The objective of the kNN single method is to verify whether a point of interest (POI) n i obtained from a peer is a valid (i.e., top k) nearest neighbor of a mobile host q. To this end we utilize the spatial relationship between mobile hosts and their POIs as follows. q p1 n1 n2 n3 ||q, p1|| ||q, n2|| + ||q, p1|| < ||p1, n3|| r Cq Cp1 Figure 2. POI n 2 is verified as a valid NN of mobile host q. Lemma 3.1 Let q and p 1 be two mobile hosts, and let p 1 have k nearest neighbors, n 1 ,n 2 ,...,n k , which are sorted in ascending order according to their distance to p 1 . For any nearest neighbor n i of p 1 ,if ||q,n i ||+||q,p 1 || ≤ ||p 1 ,n k || then n i is one of the top k-nearest neighbors of q. ||q,n i ||, ||q,p 1 ||, and ||p 1 ,n k || are the Euclidean dis- tances between q and n i , q and p 1 , and p 1 and its cached farthest nearest neighbor n k , respectively. Proof: Assume n i / ∈ kNN of q and n i ∈ kNN of p 1 . Then, there exist m 1 ,m 2 ,...,m k ∈ kNN of q such that ∀m i ∈ {m 1 ,m 2 ,...,m k }, ||q,m i || < ||q,n i ||. We can identify a point r located at the intersection of the extension of the line from p 1 to q and the circumference of the circle with center q and radius||q,n i || (identified as circle C q in Fig. 2). Then, ∀m i ∈ kNN of q: ||p 1 ,m i || <||p 1 ,r|| (1) Recall that we assume the following inequality holds: ||q,n i ||+||q,p 1 || ≤ ||p 1 ,n k || (2) Because the circle C q is fully covered by the circle C p1 (with center p 1 and radius||p 1 ,r||), it follows that ||q,n i ||+||q,p 1 || =||q,r||+||q,p 1 || =||p 1 ,r|| (3) By Equations 1, 2 and 3, ∀m i ∈ kNN of q, ||p 1 ,m i || < ||p 1 ,n k ||. Thus n k / ∈ kNN of p 1 . However, this contradicts the assumption that n k ∈ kNN of p 1 . Therefore, n i must be one of the top k-nearest neighbors of q. Verified/Unverified V V UV UV Points of interest n2−p1 n1−p1 n3−p1 n3−p2 Distance to q (examples) √ 2 √ 3 √ 5 √ 8 Table 2. The data structure of the heap H. An illustration of Lemma 3.1 is shown in Figure 2. The nearest neighbor n 2 of mobile host p 1 , which is a peer of mobile host q, can be verified as the nearest neighbor of q and is termed a verified nearest neighbor. This holds because the Euclidean distance between n 2 and q plus the Euclidean distance between q and p 1 is no greater than the Euclidean distance between p 1 and its presently cached far- thest nearest neighbor n 3 . The exact ranking of nearest neighbors can also be obtained (see detailed proof in [10]). The kNN single method maintains a heap H with the en- tries of verified and unverified points of interest discovered so far (illustrated in Table 2). The size of H is determined by the total number of queried interest objects q k . Initially H is empty and the kNN single method sequentially processes the result set P of nearest neighbor objects from mobile hosts in the vicinity of q. For each POI the heap H is updated with the distance from the location of q to the POI object and its validity. If there exist unverified nearest neighbor objects in H, a newly discovered verified NN object will replace an unverified object and H maintains the verified objects in an ascending order of their Euclidean distance to q. Unveri- fied objects exist in H only if the number of verified objects is less than q k . These unverified objects are also stored in ascending distance order. Consider the following example to illustrate the operation of kNN single . Figure 3 illustrates the location of q and its two closest mobile hosts, p 1 and p 2 . The single peer NN ver- ification rule follows Lemma 3.1. Assuming that q searches for four nearest neighbors, then after processing p 1 and p 2 the content of the heap H is as shown in Table 2. Based on the set P which contains peers p 1 and p 2 , q can retrieve two verified NNs, n 2−p1 and n 1−p1 , and two unverified NNs, n 3−p1 and n 3−p2 . kNN single is executed iteratively for each peer in the nearest neighbor result set P.If k elements in H are veri- fied, the kNN query is fulfilled and H will remember the top k NN in sequence. Otherwise, we must expand the search space to include more candidate interest objects. This is accomplished by the kNN multiple algorithm, which is de- scribed next. The single peer NN verification procedure is summarized in Algorithm 1. 3.2.2 Step 2: Multiple Peer NN Verification Under some conditions the kNN single method may not be able to verify all k nearest neighbors. Therefore, we ex- tend the verification process to include results from mul- tiple peers simultaneously. Figure 4 demonstrates an ex- ample in which a point of interest (n 2−p3 ) cannot be veri- fied by kNN single : neither with peer p 3 nor with peer p 4 . The kNN multiple method combines the verified regions of all the peers, each bounded by the outermost NN circle, into a merged verified region R v (the shaded area in Figure 4c). It is computationally expensive to compute an exact solution Algorithm 1 kNN single (q, p, k) 1: H←∅ 2: n far ← the farthest node in p.N 3: for∀n i ∈ p.N and|H.verified|<k do 4: if ||(q,n i )||+||(q,p)|| ≤ ||(p,n far )|| then 5: H.verified∪ = n i 6: else 7: if|H|<k then 8: H.unverified∪ = n i 9: else if∃n j and||(q,n j )|| > ||(q,n i )|| where n j ∈ H.unverified then 10: replace n j in H.unverified with n i 11: end if 12: end if 13: end for 14: return H for R v . Therefore, we adopt a polygonization technique that transforms the verified region of each peer (p.R) into poly- gons as a close approximation. After this transformation the polygons can be merged together into a merged verified re- gion R v by performing the MapOverlay algorithm [6] (line 3 of Algorithm 2). The kNN multiple verification technique is executed with R v providing an area bound similarly to the kNN single case. Lemma 3.2 provides the rules for verifying nearest neighbors with multiple peers and the multiple peer NN verification procedure is formalized in Algorithm 2. Lemma 3.2 If the nearest neighbor data set P is composed of data from j peers, the merged verified region R v can be represented as: R v = p 1 .R∪ p 2 .R∪···∪ p j .R. For any point of interest n i in R v , the distance between q and n i is used as a radius to create a circle C ni .If C ni is fully covered by R v , then n i is a verified NN of q. There will be cases when neither kNN single nor kNN multiple can fulfill a kNN query. Hence a set which contains unverified elements is returned. If the response time is critical, a user may agree to accept a kNN data set with unverified elements, where the objects are not guaran- teed to be the top k nearest neighbors. Otherwise the kNN query must be forwarded to a spatial database server (Step 3). The partial results in H can be used to bound and hence speed up the server search process. 3.2.3 Step 3: Server kNN Query with Pruning Bounds We assume that the spatial database server executes an ef- ficient k-nearest neighbor search algorithm based on R-tree indexing [9] for solving kNN queries. The NN search is supported with a priority queue containing the nodes vis- ited so far. Initially the priority queue contains the entries of q p1 n1-p1 n2-p1 n3-p1 p2 n1-p2 n2-p2 n3-p2 q p1 n1-p1 n2-p1 n3-p1 Fig. 3a. Mobile host q retrieves two verified nearest neighbors from the NN set of peer p 1 . Fig. 3b. Mobile host q can only retrieve unver- ified nearest neighbors from peer p 2 . Figure 3. The mobile host q and its two closest peers, p 1 and P 2 . p3 n1-p3 n2-p3 q n3-p3 cp3 p4 n2-p3 n2-p4 p4 n1-p4 q cp4 p3 p3 n2-p3 n2-p4 p4 q n3-p3 and n1-p4 n1-p3 cp3 cp4 Fig. 4a. Mobile host q can- not verify the point of interest n 2−p3 as a verified NN with peer p 3 . Fig. 4b. Mobile host q can- not verify the point of interest n 2−p3 as a verified NN with peer p 4 , either. Fig. 4c. After merging the ver- ified regions of peer p 3 and p 4 , the point of interest n 2−p3 can be verified as a valid object. Figure 4. An example of the multiple peers NN verification process. The point of interest n 2−P3 can only be verified asaNNof q based on the merged verified region of both peer p 3 and peer p 4 . Algorithm 2 kNN multiple (q, H, P , k) 1: R v ←∅ 2: for∀p ∈ P do 3: R v ∪ = p.R 4: end for 5: for∀p ∈ P and|H.verified|<k do 6: for∀n i ∈ p.N and n i / ∈ H.verified do 7: C ni ← create a circle region with ||q,n i || as the radius and q as the center point 8: if c ni ⊂ R v and|H.verified|<k then 9: H.verified∪ = n i 10: end if 11: end for 12: end for 13: return H the R-tree root sorted according to their minimum distance (MINDIST) to the query point q. In general most of the moving objects have executed either one or both kNN single and kNN multiple processes before forwarding kNN search queries to the server. Hence, it is worthwhile to calculate branch expanding upper and lower bounds from the entries in heap H to speed up the NN search process at the server. The heap H is in one of six different states after a mo- bile host has executed both the kNN single and kNN multiple mechanisms without retrieving k verified objects: • State 1: H is full and contains both verified and unver- ified entries. • State 2: H is full and contains only unverified entries. • State 3: H is not full and contains both verified and unverified entries. • State 4: H is not full and contains only verified entries. • State 5: H is not full and contains only unverified en- tries. • State 6: H contains no entry. In State 1 there may exist some POIs which are closer to q compared with the last element in H. Hence, we can consider the last entry of H as the final candidate nearest neighbor in the NN search and forward its distance attribute to the server as the branch expanding upper bound. In ad- dition, the distance attribute d v of the last verified entry can be another bound, the branch expanding lower bound. Be- cause we are certain about the POIs within the circle region C r with radius d v and center point q, the NN search algo- rithm executed in the server does not need to expand any minimum bounding rectangle which is completely covered by C r . Conversely, when H is full and contains only unver- ified entries, we can infer only the upper bound (State 2). In States 3 and 4 there have been less than k interest objects found. Therefore, we can only infer the lower bound from the distance attribute of the last verified element in H.In the last two states, H is not full and contains only unverified entries or no entry at all. Consequently we cannot infer any bounds in these cases. To take advantage of the two new bounds for kNN queries, we slightly modified the kNN best-first search al- gorithm such that it calculates one more metric for prun- ing R-tree branches: the maximum distance (MAXDIST). MAXDIST indicates which MBRs are totally covered in re- gion C r and hence no expansion is needed. Furthermore, we added two new MBR pruning strategies for the kNN search as follows: 1. Any MBR m with MAXDIST(q, m) smaller than the branch expanding lower bound is pruned. 2. Any MBR m with MINDIST(q, m) greater than the Euclidean distance from q to the k th element in H is discarded. The complete procedure of performing the SBNN sharing based kNN search is described in Algorithm 3. 4 Experimental Validation To ascertain the performance of our approach we have implemented the sharing based spatial query algorithms within a simulation environment. In addition to enabling robust and decentralized applications, the objective of our peer-to-peer design is to increase scalability in two dimen- sions. First, the server access workload can be reduced as queries are answered directly by peers. Second, for the re- maining queries that must be sent to the server, our tech- nique diminishes the search overhead by providing pruning- bounds for the kNN search algorithm. Consequently, the focus of our simulations is on quantifying the server load variations as a function of two main parameters, the spa- tial query request rate (SQRR) and the page access rate (PAR). SQRR quantifies what percentage of the client spa- tial query requests are processed by the central database Parameter Description POI Number The number of point of interest in the system MH Number The number of mobile hosts in the simulation area C Size The cache capacity of each mobile host M Percentage The mobile host movement percentage M Velocity The mobile host movement velocity (mph) λ Query The mean number of queries per minute Tx Range The transmission range of queries λ kNN The mean number of queried nearest neighbors T execution The length of a simulation run Table 3. Parameters for the simulation environment. server, and PAR denotes the server side memory (primary and secondary) access rate for a sequence of spatial queries. We have performed our experiments with both synthetic and real-world parameter sets. 4.1 Simulator Implementation Our simulator consists of two main modules, the mobile host module and the server module. The former generates and controls the movements and query launch patterns of all mobile hosts. Each mobile host (MH) is an independent ob- ject which decides its movement autonomously. The server module processes spatial searches and is responsible for es- timating the I/O load of the spatial database server. Spatial data indexing is provided with the well known R*-tree algo- rithm [1]. We implemented our SBNN query algorithm in the mobile host module. Each MH is implemented as an independent object that encapsulates all its related parameters such as the movement velocity M Velocity , the cache capacity C Size , the wireless Algorithm 3 SBNN(q, k) 1: H←∅;P ← peer nodes responding the query request issued from q. 2: for∀p ∈ P and|H.verified|<k do 3: H ∪ = kNN single (q, p, k) (Step 1) 4: end for 5: if|H.verified|<k then 6: H ∪ = kNN multiple (q, H, P , k) (Step 2) 7: end if {if k verified NN have been retrieved, or the heap is full and q accepts unverified results.} 8: if (|H.verified| = k)or(|H| = k and accept = true) then 9: return H 10: end if {if H is not full or q denies any unverified results, for- ward the query with the branch expanding upper and lower bounds to the database server.} 11: H ← kNN query results returned from the server. (Step 3) 12: return H transmission range Tx Range , etc. All MHs move inside a geographical area, measuring 30 miles by 30 miles. Ad- ditionally, user adjustable parameters are provided for the simulation such as execution length, the number of POIs, the number of mobile hosts and their query frequency, and more. Table 3 lists all of the simulation parameters. The simulation is initialized by randomly choosing a starting location for each mobile host within the simulation area. Mobile hosts follow an underlying road network and their travel speed s is determined by the speed limit on the corresponding road segment. We employ the random way- point model [2] to determine mobility. Each MH selects a random destination point inside the simulation area and pro- gresses towards it. When reaching that location, it pauses for a random interval and decides on a new destination for the next travel period. This process repeats for all MHs until the end of the simulation. Every simulation has numerous intervals (whose lengths are Poisson distributed) and during each interval the simula- tor selects a random subset of the mobile hosts to launch spa- tial queries (the query intervals are also based on a Poisson distribution). The subset size is controlled via the λ Query parameter (e.g., 1,000 queries per minute). These hosts then execute the SBNN algorithm by interacting with their peers. A mobile host will first attempt to answer each spa- tial query via the kNN single and kNN multiple approaches. If this is unsuccessful, the query will be forwarded to the remote database server. Each mobile host manages its local NN query result cache with a combination of the following two policies: 1. A MH only stores the query location (the coordinates where it launched the query) and all the verified nearest neighbors of the most recent query. 2. If a kNN query must be sent to the server, the MH will query for as many NNs as its cache capacity al- lows (e.g., if the cache capacity is 20, the query will be for 20-NNs). The single peer nearest neighbor verification process is implemented according to the algorithm detailed in Sec- tion 3.2.1. A mobile host sequentially verifies the candi- date points of interest starting with the results obtained from its closest peer query location (using Euclidean distance). In the multiple peer verification algorithm of Section 3.2.2, multiple, potentially overlapping circles must be combined to provide the verification area. We utilize a polygoniza- tion technique that transforms all the peer verified region cir- cles into polygons and then sequentially combines them into a merged verified region R v by performing the MapOver- lay algorithm. Afterwards, a MH can verify POIs with the kNN multiple verification technique based on the R v area. Parameter Los Angeles Riverside Synthetic Units County County Suburbia POI Number 4050 2160 3105 MH Number 121500 11700 66600 CSize 20 20 20 MPercentage 80 80 80 % M Velocity 30 30 30 mph λQuery 8100 780 4440 min −1 TxRange 200 200 200 m λ kNN 5 5 5 Texecution 5 5 5 hr Table 4. The simulation parameter sets for Los An- geles Count, Riverside County, and Synthetic Sub- urbia. 4.1.1 Simulation Parameter Sets To obtain results that closely correspond to real world con- ditions we obtained our simulation parameters from public data sets, for example, car and gas station densities in ur- ban areas. We term the two parameter sets based on these real-world statistics the Los Angeles County and the River- side County parameter sets, respectively. The details of the parameters were as follows. • Points of Interest: We obtained information about the density of interest objects (e.g., gas stations, restau- rants, hospitals, etc.) in the Greater Los Angeles area from two online sites: GasPriceWatch.com 2 and CNN/Money. Because gas stations are commonly the target of kNN queries, we use them as the sample POI type for our simulations. The server load variations of other POI types are expected to be similar. • Mobile Hosts: We collected vehicle statistics of the Greater Los Angeles area from the Federal Statistics web site. The data provide the number of registered vehicles in the Los Angeles and Riverside Counties (5,498,554 and 944,645, respectively). In our simula- tions we assume that about 10% of these vehicles are on the road during non-peak hours according to the traffic information from Caltrans 3 . We further obtained the land area of each county to compute the average vehi- cle density per square mile. The Los Angeles and the Riverside County parame- ter sets represent a very dense, urban area and a low- density, more rural area. Hence, for comparison purposes we blended the two real parameter sets to generate a third, synthetic set. The synthetic data set demonstrates vehicle and interest object densities in-between Los Angeles County and Riverside County, representing a suburban area. Table 4 lists the three parameter sets. 2 http://www.gaspricewatch.com 3 http://www.dot.ca.gov/hq/traffops/saferesr/trafdata/ 0 20 40 60 80 100 120 20 40 60 80 100 120 140 160 180 200 Transmission Range (Meters) Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Queries Solved by Multi-Peer 0 20 40 60 80 100 120 20 40 60 80 100 120 140 160 180 200 Transmission Range (Meters) Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Queries Solved by Multi-Peer 0 20 40 60 80 100 120 20 40 60 80 100 120 140 160 180 200 Transmission Range (Meters) Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Queries Solved by Multi-Peer Fig. 5a. Los Angeles County. Fig. 5b. Synthetic Suburbia. Fig. 5c. Riverside County. Figure 5. The percentage of queries that are resolved by one peer, multiple peers and the server as a function of the wireless transmission range. 0 20 40 60 80 100 120 20 16 12 8 4 Number of Cached Items Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Method Queries Solved by Multi-Peer Method 0 20 40 60 80 100 120 20 16 12 8 4 Number of Cached Items Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Method Queries Solved by Multi-Peer Method 0 20 40 60 80 100 120 20 16 12 8 4 Number of Cached Items Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Method Queries Solved by Multi-Peer Method Fig. 6a. Los Angeles County. Fig. 6b. Synthetic Suburbia. Fig. 6c. Riverside County. Figure 6. The percentage of queries that are resolved by one peer, multiple peers and the server as a function of the mobile host cache capacity. 4.2 Experimental Results We used all three input parameter sets – Los Angeles County, Riverside County, and Synthetic Suburbia – to sim- ulate our peer sharing techniques in conjunction with the simulator’s road network mode. We varied the following parameters to observe their effects on the system perfor- mance: the wireless transmission range, the cache capacity, the movement velocity, and the nearest neighbor number k. The performance metric in the mobile host module was SQRR. The primary difference between the three different parameter sets is the vehicle and the POI densities. Hence, we utilized the simulation to verify the applicability of our design to different geographical and urban areas. All simula- tion results were recorded after the system reached a steady state. 4.2.1 Effect of the Transmission Range In our first experiment we varied the mobile host wireless transmission range from 10 to 200 meters, with all other pa- rameters unchanged. We chose 200 meters as a practical upper limit on the transmission range of the IEEE 802.11 technology. Although the reliable coverage range for IEEE 802.11 in open space with good antennas can be more than 300 meters [7], obstacles such as buildings could diminish the range to 200 meters or less in urban areas. Figure 5 illus- trates the percentage of the queries that can be resolved by one peer, multiple peers or the server with the Los Angeles County, the Synthetic Suburbia, and the Riverside County parameter sets, respectively. As the transmission range ex- tends, an increasing number of queries can be answered by surrounding peers. As expected, the effect is most pro- nounced in Los Angeles County, because of its high vehicle density. With a transmission range of 200 meters less than 20% of the queries must be sent to the server. 4.2.2 Effect of the MH Cache Capacity Next we varied the mobile host cache capacity, which de- notes how many nearest neighbor objects a mobile host can store. Figure 6 illustrates cache capacities from 4 to 20 with the three parameter sets. In Figure 6a, even though the num- ber of interest objects is much larger than the maximum capacity of the cached NN query results, we observe a re- markable server workload decrease with a higher MH cache capacity. 4.2.3 Effect of the MH Movement Velocity We studied the effect of the host movement velocity by changing the MH speed from 10 miles per hour (mph) to 50 mph and the results are shown in Figure 7. We observe that the movement velocity has a stronger effect on the server 0 20 40 60 80 100 120 10 15 20 25 30 35 40 45 50 Mobile Host Speed (Mph) Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Queries Solved by Multi-Peer 0 20 40 60 80 100 120 10 15 20 25 30 35 40 45 50 Mobile Host Speed (Mph) Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Queries Solved by Multi-Peer 0 20 40 60 80 100 120 10 15 20 25 30 35 40 45 50 Mobile Host Speed (Mph) Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Queries Solved by Multi-Peer Fig. 7a. Los Angeles County. Fig. 7b. Synthetic Suburbia. Fig. 7c. Riverside County. Figure 7. The percentage of queries that are resolved by one peer, multiple peers and the server as a function of the mobile host movement velocity. 0 20 40 60 80 100 120 15 12 9 6 3 Number of k Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Method Queries Solved by Multi-Peer Method 0 20 40 60 80 100 120 15 12 9 6 3 Number of k Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Method Queries Solved by Multi-Peer Method 0 20 40 60 80 100 120 15 12 9 6 3 Number of k Percentage of Total Queries Queries Solved by the Server Queries Solved by Single-Peer Method Queries Solved by Multi-Peer Method Fig. 8a. Los Angeles County. Fig. 8b. Synthetic Suburbia. Fig. 8c. Riverside County. Figure 8. The percentage of queries that are resolved by one peer, multiple peers and the server as a function of k. workload in areas with a lower vehicle and interest object density. However, the effect is quite gradual in all cases. 4.2.4 Effect of k We were also interested in the effect that varying the num- ber of requested nearest neighbors, i.e., k, would have on the system performance. In our simulation we chose k ran- domly for each host and each query in the range from 3 to 15. Figure 8 illustrates the results. The server workload of the Los Angeles County parameter set increases 29% when we raise k from 3 to 15. The server workload of the River- side County parameter set increases by only 19%, because its starting level is much higher. Not surprisingly result shar- ing is much more effective for small values of k. 4.3 ImpactofPruningBoundsonPerformance of Spatial Database Server In order to evaluate the nearest neighbor query pruning bounds of Section 3.2.3, we extended the R-tree incremen- tal nearest neighbor (INN) algorithm [9] with one more met- ric, MAXDIST. For each incoming NN query from mobile hosts, the server module executes both the original INN algorithm and our extended INN algorithm with pruning bounds (denoted EINN) to compare the performance im- provement with respect to page accesses. We examined the behavior of the two algorithms as the number of k increased. We utilized the R*-tree for indexing the POI data set (gas station locations) in the server module. The R*-tree has an advantage in query response time over the conventional R- tree algorithm by utilizing more sophisticated insertion and node-splitting methods, which attempt to minimize a com- bination of overlap between bounding rectangles and the to- tal area. The branching factor of both the index and leaf nodes was set to 30. Because NN queries are generated by randomly selected mobile hosts, query points are uniformly distributed over the simulation area. The experiments were executed sufficiently often to obtain consistent results. At the ends of the performance spectrum there are two extreme I/O behaviors of the spatial database server: all re- quested memory pages are found in main memory or every I/O leads to disk activity. In the former case, because of fast main memory access, we cannot discern a significant per- formance difference between INN and EINN. However, any reasonably large data set will not fit into main memory and more disk I/Os will be performed. Hence, the database I/O behavior is closer to the other end of the spectrum. Since the EINN usually requests fewer R*-tree nodes and objects than INN, we believe that the kNN search algorithm with query pruning bounds (EINN) will have good scalability with large data sets. During the simulation process, the server module counted the number of R*-tree node (index nodes and data nodes) accesses which corresponded to both main memory and disk I/Os. According to our observation, the number of node accesses provides a good predication of the actual NN query I/O cost. 0 5 10 15 20 25 30 4 6 8 10 12 14 Number of of k R*-tree pages accessed EINN (LA) INN (LA) EINN (SYN) INN (SYN) EINN (RV) INN (RV) Figure 9. The page access comparison of EINN and INN as a function of k. Next, we varied the number of k with all the three pa- rameter sets with both the EINN and INN algorithms. The server module recorded the relevant R*-tree page access in- formation (Section 4.2.4). As shown in Figure 9, the EINN algorithm performs consistently better than INN, while the rate of growth is similar for both. We conclude that the pruning bounds can always decrease the number of page ac- cesses. We varied the number of k from 3 to 15 with the three parameter sets and the EINN algorithm accesses 10% to 21% fewer pages than INN. We conclude from all the performed experiments that the mobile host density has a considerable impact on the spatial query request rate. As a result, if more mobile hosts travel in a specific area, each MH has a higher opportunity to fulfill its kNN queries by peers. Furthermore, the nearest neighbor query pruning bounds also have a significant positive effect on the page access rate and successfully decrease the server load. 5 Conclusions and Future Work We have presented a novel approach for answering spatial nearest neighbor search queries by leveraging results from neighboring peers within a mobile environment. Signifi- cantly, our method allows a mobile peer to locally verify whether candidate objects received from neighbors are in- deed part of its own nearest neighbor data set. Our simula- tion results indicate that the technique can reduce the access traffic to remote servers by a considerable amount, for ex- ample up to 80% in a dense urban area. This is achieved with minimal caching at the peers. By virtue of its peer- to-peer architecture, the method exhibits great scalability: the higher the mobile peer density, the more queries can be answered by peers. Therefore, the load on the remote data- bases increases sub-linearly with the number of clients. We plan to extend our work to investigate other types of spatial queries, such as range and spatial join searches. References [1] Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, and Bernhard Seeger. The R*-tree: An Efficient and Robust Ac- cess Method for Points and Rectangles. In Proceedings of the ACM SIGMOD International Conference on Management of Data, pages 322–331, 1990. [2] Josh Broch, David A. Maltz, David B. Johnson, Yih-Chun Hu, and Jorjeta Jetcheva. A Performance Comparison of Multi-Hop Wireless Ad Hoc Network Routing Protocols. In Proceedings of the 4 th ACM/IEEE MobiCom, pages 85–97, 1998. [3] Chi-Yin Chow, Hong Va Leong, and Alvin Chan. Peer-to- Peer Cooperative Caching in Mobile Environment. In Pro- ceedings of the 24 th International Conference on Distributed Computing Systems Workshops, pages 528–533, 2004. [4] Chi-Yin Chow, Hong Va Leong, and Alvin T. S. Chan. Group-based Cooperative Cache Management for Mobile Clients in a Mobile Environment. In Proceedings of the In- ternational Conference on Parallel Processing (ICPP), Mon- treal, Quebec, Canada, August 15-18, 2004. [5] M. Dahlin, R. Y . Wang, T. E. Anderson, and D. A. Patter- son. Cooperative caching: Using remote client memory to improve file system performance. In Procedings of the 1 st USENIX OSDI, pages 267–280, November 1994. [6] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry Algorithms and Applications (2nd Edition). Springer, 2000. [7] Gregor Gaertner and Vinny Cahill. Understanding link qual- ity in 802.11 mobile ad hoc networks. IEEE Internet Com- puting, 8(1):55–60, 2004. [8] Antomn Guttman. R-Trees: A Dynamic Index Structure for Spatial Searching. In Proceedings of the ACM SIGMOD In- ternational Conference on Management of Data, pages 47– 57, Boston, Massachusetts, June 18-21, 1984. [9] G´ ısli R. Hjaltason and Hanan Samet. Distance browsing in spatial databases. ACM Trans. Database Syst., 24(2):265– 318, 1999. [10] Wei-Shinn Ku, Roger Zimmermann, and Chi-Ngai Wan. Location-based Spatial Queries with Data Sharing in Mobile Environment. Technical Report USC-CS-TR05-843, Univer- sity of Southern California, 2005. [11] Nick Roussopoulos, Stephen Kelley, and Fr´ ed´ eric Vincent. Nearest Neighbor Queries. In Proceedings of the 1995 ACM SIGMOD International Conference on Management of Data, pages 71–79, San Jose, CA, May 22-25, 1995. [12] Zhexuan Song and Nick Roussopoulos. k-Nearest Neighbor Search for Moving Query Point. In Proceedings of Advances in Spatial and Temporal Databases, 7 th International Sympo- sium (SSTD), pages 79–96, Redondo Beach, CA, July 12-15, 2001. [13] D. Wessels and K. Claffy. ICP and the Squid Web Cache. IEEE Journal on Selected Areas in Communications (JSAC), pages 345–357, March 1998.

Linked assets

Computer Science Technical Report Archive

Conceptually similar

PDF

USC Computer Science Technical Reports, no. 843 (2005)

PDF

USC Computer Science Technical Reports, no. 871 (2005)

PDF

USC Computer Science Technical Reports, no. 892 (2007)

PDF

USC Computer Science Technical Reports, no. 909 (2009)

PDF

USC Computer Science Technical Reports, no. 908 (2009)

PDF

USC Computer Science Technical Reports, no. 959 (2015)

PDF

USC Computer Science Technical Reports, no. 628 (1996)

PDF

USC Computer Science Technical Reports, no. 878 (2006)

PDF

USC Computer Science Technical Reports, no. 625 (1996)

PDF

USC Computer Science Technical Reports, no. 781 (2002)

PDF

USC Computer Science Technical Reports, no. 891 (2007)

PDF

USC Computer Science Technical Reports, no. 699 (1999)

PDF

USC Computer Science Technical Reports, no. 762 (2002)

PDF

USC Computer Science Technical Reports, no. 899 (2008)

PDF

USC Computer Science Technical Reports, no. 685 (1998)

PDF

USC Computer Science Technical Reports, no. 852 (2005)

PDF

USC Computer Science Technical Reports, no. 739 (2001)

PDF

USC Computer Science Technical Reports, no. 627 (1996)

PDF

USC Computer Science Technical Reports, no. 964 (2016)

PDF

USC Computer Science Technical Reports, no. 911 (2009)

Description

Wei-Shinn Ku, Roger Zimmermann, Chi-Ngai Wan. "Nearest neighbor queries with data sharing in mobile environments." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 886 (2006).

Asset Metadata

Creator Ku, Wei-Shinn (author), Wan, Chi-Ngai (author), Zimmermann, Roger (author)

Core Title USC Computer Science Technical Reports, no. 886 (2006)

Alternative Title Nearest neighbor queries with data sharing in mobile environments (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

Tag OAI-PMH Harvest

Format 10 pages (extent), technical reports (aat)

Language English

Unique identifier UC16269805

Identifier 06-886 Nearest Neighbor Queries with Data Sharing in Mobile Environments (filename)

Legacy Identifier usc-cstr-06-886

Format 10 pages (extent),technical reports (aat)

Rights Department of Computer Science (University of Southern California) and the author(s).

Internet Media Type application/pdf

Source 20180426-rozan-cstechreports-shoaf (batch), Computer Science Technical Report Archive (collection), University of Southern California. Department of Computer Science. Technical Reports (series)

Access Conditions The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Repository Email csdept@usc.edu

Inherited Values

Title Computer Science Technical Report Archive

Description Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017.

Coverage Temporal 1991/2017

Repository Email csdept@usc.edu

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)