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Conference papers

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

Ittai Abraham 1 Shiri Chechik 2 Cyril Gavoille 3, 4, 5
4 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
CNRS - Centre National de la Recherche Scientifique : UMR5800, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Inria Bordeaux - Sud-Ouest, Université Sciences et Technologies - Bordeaux 1
Abstract : This paper considers fully dynamic (1 + ε) distance oracles and (1 + ε) forbidden-set labeling schemes for pla- nar 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 log2 n log (nM ) * (ε−1 + log n)). 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|2λ) 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 * (ε−1 + log n)) and has O ̃(n1/2) 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 O ̃(n2/3) and amortized update time of O ̃(n2/3). Our (1 + ε) forbidden-set labeling scheme can also be extended into a forbidden-set labeled routing scheme with stretch (1 + ε).
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Contributor : Cyril Gavoille Connect in order to contact the contributor
Submitted on : Monday, August 27, 2012 - 11:48:46 PM
Last modification on : Friday, February 4, 2022 - 3:14:50 AM




Ittai Abraham, Shiri Chechik, Cyril Gavoille. Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels. 44th Annual ACM Symposium on Theory of Computing (STOC), May 2012, New-York, United States. pp.1199-1217, ⟨10.1145/2213977.2214084⟩. ⟨hal-00725839⟩



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