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Maximum weight independent set in trees

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Abstract

Computing a maximum independent set, weighted or unweighted, isNP-hard for general as well as planar graphs. However, polynomial time algorithms do exist for solving this problem on special classes of graphs. In this paper we present an efficient algorithm for computing a maximum weight independent set in trees. A divide and conquer approach based on centroid decomposition of trees is used to compute a maximum weight independent set withinO(n logn) time, wheren is the number of vertices in the tree. We introduce a notion of analternating tree which is crucial in obtaining a new independent set from the previous one.

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Authors and Affiliations

  1. Department of Computer Science, SUNY at Stony Brook, 11794, Stony Brook, NY, U.S.A.

    Shaunak Pawagi

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  1. Shaunak Pawagi
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Pawagi, S. Maximum weight independent set in trees. BIT 27, 170–180 (1987). https://doi.org/10.1007/BF01934182

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  • DOI: https://doi.org/10.1007/BF01934182

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