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A Faster Algorithm for Finding Disjoint Paths in Grids

  • Wun-Tat Chan
  • Francis Y. L. Chin
  • Hing-Fung Ting
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

Given a set of sources and a set of sinks in the two dimensional grid of size n, the disjoint paths (DP) problem is to connect every source to a distinct sink by a set of edge-disjoint paths. Let v be the total number of sources and sinks. In [3], Chan and Chin showed that without loss of generality we can assume vn ≤ 4v 2. They also showed how to compress the grid optimally to a dynamic network (structure of the network may change depending on the paths found currently) of size \( O(\sqrt {nv} ) \) , and solve the problem in \( O(\sqrt n v^{3/2} ) \) time using augmenting path method in maximum flow. In this paper, we improve the time complexity of solving the DP problem to O(n 3/4 v 3/4). The factor of improvement is as large as \( \sqrt v \) when n is (itv), while it is at least \( \sqrt[4]{v} \) for n is (v 2).

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Wun-Tat Chan
    • 1
  • Francis Y. L. Chin
    • 1
  • Hing-Fung Ting
    • 1
  1. 1.Department of Computer Science and Information SystemsThe University of Hong KongHong Kong

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