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A Linear Time Algorithm for the Minimum Spanning Caterpillar Problem for Bounded Treewidth Graphs

  • Michael J. Dinneen
  • Masoud Khosravani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6058)

Abstract

We consider the Minimum Spanning Caterpillar Problem (MSCP) in a graph where each edge has two costs, spine (path) cost and leaf cost, depending on whether it is used as a spine or a leaf edge. The goal is to find a spanning caterpillar in which the sum of its edge costs is the minimum. We show that the problem has a linear time algorithm when a tree decomposition of the graph is given as part of the input. Despite the fast growing constant factor of the time complexity of our algorithm, it is still practical and efficient for some classes of graphs, such as outerplanar, series-parallel (K 4 minor-free), and Halin graphs. We also briefly explain how one can modify our algorithm to solve the Minimum Spanning Ring Star and the Dual Cost Minimum Spanning Tree Problems.

Keywords

spanning caterpillars treewidth networks topology optimization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Michael J. Dinneen
    • 1
  • Masoud Khosravani
    • 1
  1. 1.Department of Computer ScienceThe University of AucklandAucklandNew Zealand

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