Abstract

We initiate the algorithmic study of an important but NP-hard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem v , for each source node v. (2) A small set of cable types, where each cable type is specified by its capacity and its cost per unit length. The cost per unit capacity per unit length of a high-capacity cable may be significantly less than that of a low-capacity cable, reflecting an economy of scale, i.e., the payoff for buying at bulk may be very high. The goal is to design a minimum-cost network that can (simultaneously) route all the demands at the sources to the sink, by installing zero or more copies of each cable type on each edge of the graph. An additional restriction is that the demand of each source must follow a single path. The problem is to find a route from each source node to the sink and to assign ca...

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