@inproceedings{ddb0aa27aa774888982094e009edf5fe,

title = "Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels",

abstract = "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 {\~O}(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 {\~O}(n 2/3) and amortized update time of {\~O}(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).",

keywords = "distance oracle, dynamic algorithms, planar graphs",

author = "Ittai Abraham and Shiri Chechik and Cyril Gavoille",

year = "2012",

doi = "10.1145/2213977.2214084",

language = "אנגלית",

isbn = "9781450312455",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

pages = "1199--1217",

booktitle = "STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing",

note = "null ; Conference date: 19-05-2012 Through 22-05-2012",

}