On multiroute maximum flows in networks

Let G = (N, A) be a network with a designated source node s, a designated sink node t, and a finite integral capacity uij < U on each arc (ij) E A. An elementary K-flow is a flow of K units from s to t such that the flow on each arc is 0 or 1. A K-route flow is a flow from s to t that may be expressed as a non-negative linear sum of elementary Kflows. In this paper, we show how to determine a maximum K-route flow as a sequence of O(min{log KU, K}) minimum cut problems plus a single maximum flow problem. This improves upon the algorithm by Kishimoto, which solves this problem as a sequence of K minimum cut problems plus a maximum flow problem. In addition, we have simplified and extended some of the basic theory.