Problems concerning the optimum location of various devices installed in transport, communication, and other types of networks relate to the so‐called location on network problems. In this paper, we show how an expanded multiple cover problem can be solved in polynomial time for the case of an undirected flow network, which is a special case of the location problem on flow networks. Up to now, such problems were solved in polynomial time for conditions when values of the flow to each vertex were set above a certain constant magnitude. Here, we show the possibility of solving these problems by a simple algorithm even in cases where these magnitudes are different for each vertex. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(1): 67–74, 2001

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Location theory on networks is concemed with the problem of selecting the best location in a specified network for facilities. Many studies for the theory have been done. We have studied location theory from the standpoint of measuring the closeness between two vertices by the capacity (maximum flow value) between two vertices. In the previous paper, we have considered location problems, called covering problems and proposed polynomial time algorithms for these problems. These problems are applicable to assigning files to some computers in a computer network. This paper concems a problem called plural cover problem defined in the previous paper. We define a generalized plural cover problem and we propose an efficient algorithm for the generalized plural cover problem.

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