A Faster and Flexible Algorithm for a Location Problem on Undirected Flow Networks

Hiro ITO
Hideyuki UEHARA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A    No.4    pp.704-712
Publication Date: 2000/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
graph,  network flow,  location problem,  node subset,  polynomial time,  algorithm,  

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For a given graph G=(V, E), edge capacities c(e) for edges e E, and flow-demands d(v) for nodes v V, a problem of finding the minimum size source-set S V such that the maximum flow-amount between S and v is greater than or equal to d(v) for every v V is called generalized plural cover problem (GPC). For this problem, O(np s(n,m)) time algorithm is presented, where n, m, and p is the number of nodes, edges, and different values of d(v), respectively, and s(n,m) is the time required to solve the maximum flow problem of a graph with n nodes and m edges. This algorithm also constructs a set of optimal solutions in the same time. This property is convenient for applying it to real problems, because other constraints can also be taken into account.