Improved distance oracles and spanners for vertex-labeled graphs

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Consider an undirected weighted graph G = (V,E) with |V| = n and |E| = m, where each vertex v ∈ V is assigned a label from a set of labels L = {λ 1,...,λ }. We show how to construct a compact distance oracle that can answer queries of the form: "what is the distance from v to the closest λ-labeled vertex" for a given vertex v ∈ V and label λ ∈ L. This problem was introduced by Hermelin, Levy, Weimann and Yuster [ICALP 2011] where they present several results for this problem. In the first result, they show how to construct a vertex-label distance oracle of expected size O(kn 1+1/k ) with stretch (4k-5) and query time O(k). In a second result, they show how to reduce the size of the data structure to O(knℓ 1/k ) at the expense of a huge stretch, the stretch of this construction grows exponentially in k, (2 k -1). In the third result they present a dynamic vertex-label distance oracle that is capable of handling label changes in a sub-linear time. The stretch of this construction is also exponential in k, (2.3 k-1+1). We manage to significantly improve the stretch of their constructions, reducing the dependence on k from exponential to polynomial (4k-5), without requiring any tradeoff regarding any of the other variables. In addition, we introduce the notion of vertex-label spanners: subgraphs that preserve distances between every vertex v ∈ V and label λ ∈ L. We present an efficient construction for vertex-label spanners with stretch-size tradeoff close to optimal.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2012 - 20th Annual European Symposium, Proceedings
Number of pages12
StatePublished - 2012
Externally publishedYes
Event20th Annual European Symposium on Algorithms, ESA 2012 - Ljubljana, Slovenia
Duration: 10 Sep 201212 Sep 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7501 LNCS


Conference20th Annual European Symposium on Algorithms, ESA 2012

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


Dive into the research topics of 'Improved distance oracles and spanners for vertex-labeled graphs'. Together they form a unique fingerprint.

Cite this