USC Computer Science Technical Reports, no. 797 (2003)

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Karim Seada, Ahmed Helmy, Ramesh Govindan. "On the effect of localization errors on geographic face routing in sensor networks." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 797 (2003).

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"- B + : -B/-./-0/+ # # 3 3 3#2 + # +: 3 ,3# 13 $ # + ? $ 3 3$ + A # # + : # $# 5 #+ ,9 # $ 1+ ? # 3 7 # # + ? # #+: 3 + 3# F # , 3 1 $ + ! >, 1 # ,31 , 1 , $ 1+ A# $# # 3 3+# $# 3 2,$ # 5 $1+ # $# + $ # # # # $ 2 # + ? $# 2 # 7 3# # 3 # + # # + ! # + # $ 3# # 3# + ! # + $ $ + : 3 5 $ # 3+ !" : 7 3 +"- -D/ , 1 -D/ , 01 5 2 # #3# 3 # + ! 3 # , # 3E 1 3 # +: 3 5 3 3 +: 5 3 +: , # 3 3 1 3 + 9 $ + 9 B + ' 2 2 $ + : 3 3# # + : 3 > 5 ; $ 4 , 1 5 + For each node u, where N is a list of the neighbors of u: for all v ∈ N for all w ∈ N if w == v then continue else if d(u,v)>max[d(u,w),d(w,v)] remove edge (u,v) >"- For each node u, where N is a list of the neighbors of u: for all v ∈ N for all w ∈ N if w == v then continue else if d(c,w)<d(c,u) {where c is the midpoint of edge (u,v)} remove edge (u,v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u and v are connected iff d(u,v) < R, where R is the radio range if v ∈ N d(u,v) < R, where N is the neighbor list of u if d(u,v) < R v ∈ N 9 # $ #> v ∈ N and d(u`,v`) > R (u` and v` are the estimated locations) d(u`,v`) < R and v ∉ N : 3 # $ 3# +9 2 3 $3# + !", :# $ +# , 1 $ 3 $ ,31 3$+ 9"-,1 decision{d(u,v)>max[d(u,w),d(w,v)]} ≠ decision{d(u`,v`)>max[d(u`,w`),d(w`,v`)]} ?,01 decision{d(c,w) < d(c,u)} ≠ decision{d(c`,w`) < d(c`,u`)} ,1+ ,5 1 $ +9B +9 $ +: 3 + : # > 2 , 1 2 2, 0 B1 ? $ + 9 3 3 3 > 2 , 41 2 $ 9 # $ 3 3$ + - : # 3 3 +! $ 3$ # > $ $ 3$ $ $3 $ 2+ : 3 # 3 #+ #.#/ # 5 $ $ $ 3$ # + 4 5 !G&* 5 6G&66* + # $ &* # > w such that d(u,v) > max[d(u,w),d(w,v)] & w` s.t. d(u`,v`)> max[d(u`,w`),d(w`,v`)] (where w is a neighbor of u, but not of v) d(u,v) < R, d(u,w) < R, d(w,v) > R (this condition is for disconnection between u and v to be possible, otherwise an edge (u,v) will be removed and another (w,v) added) d(u,v) < max[d(u,w),d(w,v)] ∀ w ∈ N d(u`,v`)> max[d(u`,w`),d(w`,v`)]for some w∈N 6 7 5 : 7 > $ $ ΔGH6H ,3Δ1I "- > RNG intersection equation: u circle: (x-x u ) 2 + (y-y u ) 2 < d(u,v) 2 v circle: (x-x v ) 2 + (y-y v ) 2 < d(u,v) 2 without loss of generality assume x u = 0, y u = 0, x v = r = d(u,v), y v = 0 Equation of the intersection curve: < < - < < - = 0 0 . 0 0 0 0 0 Δ > distance between w and closest point on intersection curve Δ < distance between w and furthest point on intersection curve Approximately: d(v,w) – d(u,v) < Δ (Figure 8) " Δ <>"-3 Δ J>3 3 ,J1> d(c,w)-d(u,v)/2 < Δ < d(c,w)+d(u,v)/2 3 # 3 $ 3$+ #. 00 # 9 $ $ $ 3$ # + 4 5 3$ $3$> ∃ w such that d(u,v) > max[d(u,w),d(w,v)] & w s.t. d(u`,v`) > max[d(u`,w`),d(w`,v`)] (where w is a neighbor of u and v) d(u,v) < R, d(u,w) < R, d(w,v) < R d(u,v) > max[d(u,w),d(w,v)]for some w ∈ N d(u`,v`) < max[d(u`,w`),d(w`,v`)] ∀ w ∈ N 7 5:3 "- + , 1"- > Δ > distance between w and closest point on intersection curve Δ < distance between w and furthest point on intersection curve ,31 3 > d(u,v)/2 - d(c,w) < Δ < d(u,v)/2 + d(c,w) 3 3 $ 3$+ --1 : ,"- 1 $ 2 + .>& 0 6 >& B 4 5: ++ ,&* K" &* K"1+ , # 3 $3# 1+ : + : B ,. 1+ + < 0+ &* &* 3 &* &* & > 4 5 (x,w) does not cross (u,v) (x`,w`) crosses (u`,v`) 7 5 Δ > distance to (u,v) & 0> &* &* 4 5 (x,w) does not cross (u,v) (x`,w`) crosses (u`,v`) w` is not in (u`,v`) planar intersection 7 5 Δ > distance to (u,v) + distance to closest point on (u,v) intersection curve & B>&* &* 4 5 (x,w) crosses (u,v), w is in (u,v) planar intersection (x`,w`) crosses (u`,v`) w` is not in (u`,v`) planar intersection 7 5 Δ > distance to closest point on (u,v) intersection curve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Asset Metadata

Creator Govindan, Ramesh (author), Helmy, Ahmed (author), Seada, Karim (author)

Core Title USC Computer Science Technical Reports, no. 797 (2003)

Alternative Title On the effect of localization errors on geographic face routing in sensor networks (title)

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

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Format 12 pages (extent), technical reports (aat)

Language English

Unique identifier UC16271001

Identifier 03-797 On the Effect of Localization Errors on Geographic Face Routing in Sensor Networks (filename)

Legacy Identifier usc-cstr-03-797

Format 12 pages (extent),technical reports (aat)

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

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

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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

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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