TY - GEN

T1 - Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels

AU - Abraham, Ittai

AU - Chechik, Shiri

AU - Gavoille, Cyril

PY - 2012

Y1 - 2012

N2 - This paper considers fully dynamic (1+ε) distance oracles and (1+ε) forbidden-set labeling schemes for planar graphs. For a given n-vertex planar graph G with edge weights drawn from [1,M] and parameter ε>0, our forbidden-set labeling scheme uses labels of length λ = O(ε -1 log 2n log(nM) · maxlogn). Given the labels of two vertices s and t and of a set F of faulty vertices/edges, our scheme approximates the distance between s and t in G \ F with stretch (1+ε), in O(|F| 2 λ) time. We then present a general method to transform (1+ε) forbidden-set labeling schemas into a fully dynamic (1+ε) distance oracle. Our fully dynamic (1+ε) distance oracle is of size O(n log{n} · maxlogn) and has Õ(n 1/2) query and update time, both the query and the update time are worst case. This improves on the best previously known (1+ε) dynamic distance oracle for planar graphs, which has worst case query time Õ(n 2/3) and amortized update time of Õ(n 2/3). Our (1+ε) forbidden-set labeling scheme can also be extended into a forbidden-set labeled routing scheme with stretch (1+ε).

AB - This paper considers fully dynamic (1+ε) distance oracles and (1+ε) forbidden-set labeling schemes for planar graphs. For a given n-vertex planar graph G with edge weights drawn from [1,M] and parameter ε>0, our forbidden-set labeling scheme uses labels of length λ = O(ε -1 log 2n log(nM) · maxlogn). Given the labels of two vertices s and t and of a set F of faulty vertices/edges, our scheme approximates the distance between s and t in G \ F with stretch (1+ε), in O(|F| 2 λ) time. We then present a general method to transform (1+ε) forbidden-set labeling schemas into a fully dynamic (1+ε) distance oracle. Our fully dynamic (1+ε) distance oracle is of size O(n log{n} · maxlogn) and has Õ(n 1/2) query and update time, both the query and the update time are worst case. This improves on the best previously known (1+ε) dynamic distance oracle for planar graphs, which has worst case query time Õ(n 2/3) and amortized update time of Õ(n 2/3). Our (1+ε) forbidden-set labeling scheme can also be extended into a forbidden-set labeled routing scheme with stretch (1+ε).

KW - distance oracle

KW - dynamic algorithms

KW - planar graphs

UR - http://www.scopus.com/inward/record.url?scp=84862615529&partnerID=8YFLogxK

U2 - 10.1145/2213977.2214084

DO - 10.1145/2213977.2214084

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84862615529

SN - 9781450312455

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1199

EP - 1217

BT - STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing

T2 - 44th Annual ACM Symposium on Theory of Computing, STOC '12

Y2 - 19 May 2012 through 22 May 2012

ER -