Maximal covering tree problems

Hutson and ReVelle [8] define the maximal direct covering tree problem as a bicriterion problem to identify a subtree of a given tree. The two criteria are to maximize demand covered by the subtree and to minimize the cost of the subtree. Demand at a node on the underlying tree is considered covered if it is within some prespecified covering distance S of the subtree. In the direct covering version of the problem. S = 0. In this article we present a new bicriterion formulation of the maximal direct covering tree problem and present O(n2) algorithms for solving both this problem and the special case where one must add to an existing subtree. The new formulation is extremely concise; consequently, additional constraints may be added where appropriate. This is demonstrated with the addition of a budget constraint. In addition, we demonstrate that the new formulation and algorithm can be readily extended to incorporate indirect covering (i.e., S > 0) as defined by Kim et al. [9]. © 1993 John Wiley & Sons. Inc.