The Multi-Commodity Source Location Problems and the Price of Greed
Vol. 13, no. 1, pp. 55-73, 2009. Regular paper.
Abstract Given a graph G=(V,E), we say that a vertex subset SV covers a vertex vV if the edge-connectivity between S and v is at least a given integer k, and also say that S covers an edge vwE if v and w are both covered. We propose the multi-commodity source location problem, which is such that given a vertex- and edge-weighted graph G, p players each select q vertices, and obtain a profit that is the total over all players of the weight of each player's covered vertices and edges. However, vertices selected by one player cannot be selected by the other players. The goal is to maximize the total profits of all players. We show that the price of greed, which indicates the ratio of the total profit of cooperating players to that of selfish players based on an ordered strategy, is tightly bounded by min{ p,q}. Also when k=2, we obtain tight bounds for vertex-unweighted trees when sources are located on the leaves.
Submitted: January 2008.
Reviewed: July 2008.
Revised: August 2008.
Reviewed: November 2008.
Revised: November 2008.
Reviewed: December 2008.
Revised: December 2008.
Accepted: December 2008.
Final: January 2009.
Published: February 2009.
Communicated by Md. Saidur Rahman
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