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An \(\mathcal{O}(n^4)\) Time Algorithm to Compute the Bisection Width of Solid Grid Graphs

  • Andreas Emil Feldmann
  • Peter Widmayer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Abstract

The bisection problem asks for a partition of the n vertices of a graph into two sets of size at most ⌈n/2⌉, so that the number of edges connecting the two sets is minimised. A grid graph is a finite connected subgraph of the infinite two-dimensional grid. It is called solid if it has no holes. Papadimitriou and Sideri [8] gave an \(\mathcal{O}(n^5)\) time algorithm to solve the bisection problem on solid grid graphs. We propose a novel approach that exploits structural properties of optimal cuts within a dynamic program. We show that our new technique leads to an \(\mathcal{O}(n^4)\) time algorithm.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Emil Feldmann
    • 1
  • Peter Widmayer
    • 1
  1. 1.Institute of Theoretical Computer ScienceETH ZürichSwitzerland

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