Approximating Minimum k-Tree Cover of a Connected Graph Inspired by the Multi-Ferry Routing in Delay Tolerant Networks
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Published:2023-11-16
Issue:
Volume:
Page:1-16
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ISSN:0129-0541
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Container-title:International Journal of Foundations of Computer Science
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language:en
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Short-container-title:Int. J. Found. Comput. Sci.
Affiliation:
1. Department of Information Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, 739-8527, Japan
Abstract
In this paper, we consider the problem of covering the vertex set of a given graph by [Formula: see text] trees so as to minimize the maximum weight of the trees, as a subproblem of the multi-ferry scheduling problem proposed by Zhao and Ammar. After pointing out that the approximation ratio of a greedy scheme based on the Kruskal’s algorithm is provably bad, we show that the approximation ratio cannot be better than 3/2 for [Formula: see text] even when the edge selection criterion is modified so as to minimize the increase in the maximum weight in the collection of trees. We then propose two polynomial-time algorithms with a guaranteed approximation ratio. The first algorithm achieves 3-approximation for the class of graphs in which the edge weights satisfy the triangle inequality. The second algorithm achieves 4-approximation for any connected graph with arbitrary edge weights.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Computer Science (miscellaneous)