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Approximate Distance Queries in Disk Graphs

  • Martin Fürer
  • Shiva Prasad Kasiviswanathan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4368)

Abstract

We present efficient algorithms for approximately answering distance queries in disk graphs. Let G be a disk graph with n vertices and m edges. For any fixed ε> 0, we show that G can be preprocessed in \(O(m\sqrt{n}\epsilon^{-1}+m\epsilon^{-2}\log S)\) time, constructing a data structure of size O(n 3/2 ε − 1+ − 2logS), such that any subsequent distance query can be answered approximately in \(O(\sqrt{n}\epsilon^{-1}+\epsilon^{-2}\log S)\) time. Here S is the ratio between the largest and smallest radius. The estimate produced is within an additive error which is only ε times the longest edge on some shortest path.

The algorithm uses an efficient subdivision of the plane to construct a sparse graph having many of the same distance properties as the input disk graph. Additionally, the sparse graph has a small separator decomposition, which is then used to answer distance queries. The algorithm extends naturally to the higher dimensional ball graphs.

Keywords

Short Path Sparse Graph Cluster Graph Unit Disk Graph Vertical Line Segment 
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 2007

Authors and Affiliations

  • Martin Fürer
    • 1
  • Shiva Prasad Kasiviswanathan
    • 1
  1. 1.Computer Science and EngineeringPennsylvania State University 

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