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The p-median problem on a tree T is to find a set S of p vertices on T that minimize the sum of distances from T's vertices to S. For this problem, Tamir [14] had an O(pn 2)-time algorithm, while Gavish and Sridhar [6] had an O(nlog n)-time algorithm for the case of p=2. In this paper, we study two generalizations of the 2-median problem, which are obtained… (More)

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… (More)

In this paper, we study the problem of locating a median path of limited length on a tree under the condition that some existing facilities are already located. The existing facilities may be located at any subset of vertices. Upper and lower bounds are proposed for both the discrete and continuous models. In the discrete model, a median path is not allowed… (More)

including the one proposed in [5]. Minieka showed that all the eight problems can be solved in polynomial time except the one of finding the maximum distancesum tree of a specified length, which was proved to be NP-hard later in [8]. Recently, in [6,7], Peng and Lo have proposed efficient parallel algorithms on the EREW PRAM for optimally locating in a tree… (More)