%0 Journal Article
%T An efficient algorithm for finding the semi-obnoxious $(k,l)$-core of a tree
%J Journal of Mathematical Modeling
%I University of Guilan
%Z 2345-394X
%A Motevalli, Samane
%A Fathali, Jafar
%A Zaferanieh, Mehdi
%D 2016
%\ 03/01/2016
%V 3
%N 2
%P 129-144
%! An efficient algorithm for finding the semi-obnoxious $(k,l)$-core of a tree
%K Core
%K Facility location
%K Median subtree
%K Semi-obnoxious
%R
%X In this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. Let $T=(V,E)$ be a tree. The $(k,l)$-core of $T$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. We show that, when the sum of the weights of vertices is negative, the $(k,l)$-core must be a single vertex. Then we propose an algorithm with time complexity of $O(n^2log n)$ for finding the $(k,l)$-core of a tree with pos/neg weight, which is in fact a modification of the one proposed by Becker et al. [Networks 40 (2002) 208].
%U https://jmm.guilan.ac.ir/article_1217_decabc127c158c47e815e39eb31e5c64.pdf