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A Fast Algorithm for Powerful Alliances in Trees

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Combinatorial Optimization and Applications (COCOA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6508))

Abstract

Given a graph G = (V,E) with a positive weight function w on the vertices of G, a global powerful alliance of G is a subset S of V such that for every vertex v at least half of the total weight in the closed neighborhood of v is contributed by the vertices of S. Finding the smallest such set in general graphs is NP-complete, even when the weights are all the same. In this paper, we give a linear time algorithm that finds the smallest global powerful alliance of any weighted tree T = (V,E).

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Ararat Harutyunyan

Authors
  1. Ararat Harutyunyan
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Weili Wu  & Ovidiu Daescu  & 

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Harutyunyan, A. (2010). A Fast Algorithm for Powerful Alliances in Trees. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_4

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  • DOI: https://doi.org/10.1007/978-3-642-17458-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17457-5

  • Online ISBN: 978-3-642-17458-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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