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Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error

  • Surender Baswana
  • Akshay Gaur
  • Sandeep Sen
  • Jayant Upadhyay
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)

Abstract

Thorup and Zwick, in the seminal paper [Journal of ACM, 52(1), 2005, pp 1-24], showed that a weighted undirected graph on n vertices can be preprocessed in subcubic time to design a data structure which occupies only subquadratic space, and yet, for any pair of vertices, can answer distance query approximately in constant time. The data structure is termed as approximate distance oracle. Subsequently, there has been improvement in their preprocessing time, and presently the best known algorithms [4,3] achieve expected O(n 2) preprocessing time for these oracles. For a class of graphs, these algorithms indeed run in Θ(n 2) time. In this paper, we are able to break this quadratic barrier at the expense of introducing a (small) constant additive error for unweighted graphs. In achieving this goal, we have been able to preserve the optimal size-stretch trade offs of the oracles. One of our algorithms can be extended to weighted graphs, where the additive error becomes 2 ·w max (u,v) - here w max (u,v) is the heaviest edge in the shortest path between vertices u, v.

Keywords

Short Path Weighted Graph Approximate Distance Consecutive Vertex Query Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Surender Baswana
    • 1
  • Akshay Gaur
    • 2
  • Sandeep Sen
    • 2
  • Jayant Upadhyay
    • 2
  1. 1.Department of Comp. Sc. & Engg.Indian Institute of Technology KanpurKanpurIndia
  2. 2.Department of Comp. Sc. & Engg.Indian Institute of Technology DelhiNew DelhiIndia

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