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

  • Authors:

  • Ittai Abraham;Shiri Chechik;Cyril Gavoille

  • Affiliations:

  • Microsoft Research, Silicon Valley Center, USA;Weizmann Institute, Rehovot, Israel;University of Bordeaux, Bordeaux, France

  • Venue:
  • STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
  • Year:
  • 2012

  • Student poster session

    WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science

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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 ε0, our forbidden-set labeling scheme uses labels of length λ = O(ε-1 log2n 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(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).