Efficient algorithms for a constrained k-tree core problem in a tree network

Authors:
Biing-Feng Wang;Shietung Peng;Hong-Yi Yu;Shan-Chyun Ku
Affiliations:
Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, Republic of China;Faculty of Computer and Information Sciences, Hosei University, Tokyo, Japan;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, Republic of China;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, Republic of China
Venue:
Journal of Algorithms
Year:
2006

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Abstract

Let T = (V, E) be a free tree in which each vertex has a weight and each edge has a length. Let n = |V|. Given T and parameters k and l, a (k, l)-tree core is a subtree X of T with diameter ≤ l, having k leaves, which minimizes the sum of the weighted distances from all vertices in T to X. In this paper, two efficient algorithms are presented for finding a (k, l)-tree core of T. The first algorithm has O(n2) time complexity for the case that each edge has an arbitrary length. The second algorithm has O(lkn) time complexity for the case that the lengths of all edges are 1. The (k, l)-tree core problem has an application in distributed database systems.