University of Guilan Journal of Mathematical Modeling 2345-394X 3 2 2016 03 01 An efficient algorithm for finding the semi-obnoxious $(k,l)$-core of a tree 129 144 1217 EN Samane Motevalli Faculty of Mathematics, Shahrood University, Shahrood, Iran Jafar Fathali Faculty of Mathematics, Shahrood University, Shahrood, Iran Mehdi Zaferanieh Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran Journal Article 2015 07 30 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]. https://jmm.guilan.ac.ir/article_1217_decabc127c158c47e815e39eb31e5c64.pdf