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Finding a core of a tree with pos/neg weight

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  • Mehdi Zaferanieh
  • Jafar Fathali

Abstract

Let T = (V, E) be a tree. A core of T is a path P, for which the sum of the weighted distances from all vertices to this path is minimized. In this paper, we consider the semi-obnoxious case in which the vertices have positive or negative weights. We prove that, when the sum of the weights of vertices is negative, the core must be a single vertex and that, when the sum of the vertices’ weights is zero there exists a core that is a vertex. Morgan and Slater (J Algorithms 1:247–258, 1980 ) presented a linear time algorithm to find the core of a tree with only positive weights of vertices. We show that their algorithm also works for semi-obnoxious problems. Copyright Springer-Verlag 2012

Suggested Citation

  • Mehdi Zaferanieh & Jafar Fathali, 2012. "Finding a core of a tree with pos/neg weight," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 147-160, October.
    • Handle: RePEc:spr:mathme:v:76:y:2012:i:2:p:147-160
    DOI: 10.1007/s00186-012-0394-5
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    References listed on IDEAS

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