A linear time algorithm for the minimum spanning caterpillar problem for bounded treewidth graphs

Authors:
Michael J. Dinneen;Masoud Khosravani
Affiliations:
Department of Computer Science, The University of Auckland, Auckland, New Zealand;Department of Computer Science, The University of Auckland, Auckland, New Zealand
Venue:
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Year:
2010

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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 (K4 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.