Approximate distance oracles for graphs with dense clusters

  • Authors:

  • Mattias Andersson;Joachim Gudmundsson;Christos Levcopoulos

  • Affiliations:

  • Department of Computer Science, Lund University, Lund, Sweden;Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands;Department of Computer Science, Lund University, Lund, Sweden

  • Venue:
  • ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
  • Year:
  • 2004

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Abstract

Let ${\mathcal H}_{1}=({\mathcal V},{\mathcal F}_{1}) $ be a collection of N pairwise vertex disjoint ${\mathcal O}(1)$-spanners where the weight of an edge is equal to the Euclidean distance between its endpoints Let ${\mathcal H}_{2}=({\mathcal V},{\mathcal F}_{2})$ be a graph on ${\mathcal V}$ with M edges of non-negative weight The union of the two graphs is denoted ${\mathcal G}=({\mathcal V},{\mathcal F}_{1}\cup{\mathcal F}_{2})$ We present a data structure of size ${\mathcal O}(M^{2}+|{\mathcal V}|{\rm log}|{\mathcal V}|)$ that answers (1+ε)-approximate shortest path queries in ${\mathcal G}$ in constant time, where ε0 is constant.