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

Hiro ITO, Hideyuki UEHARA, Mitsuo YOKOYAMA

Summary :

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.

• Publication: IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.4 pp.704-712
• Publication Date: 2000/04/25
• Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

Authors

Hiro ITO
Hideyuki UEHARA
Mitsuo YOKOYAMA

Keyword

graph,  network flow,  location problem,  node subset,  polynomial time,  algorithm