Two‐route flows in an undirected flow network

Abstract

This paper defines anew the maximum two‐route flow as a measure to represent the relation between two vertices in the flow network. The maximum two‐route flow corresponds to the maximum number of communication channels that are composed of two‐route paths between two terminals in a communication network. The ℱ‐rings that can be composed simultaneously, containing the considered two vertices, is defined as the maximum two‐route flow between those two vertices. It is shown in this paper that a theorem exists for the maximum two‐route flow similar to the max‐flow min‐cut theorem for the ordinary flow.

The multiroute maximum flow problem revisited

“…Therefore, we can check its feasibility by transforming it into a 1-MFP (see, e.g., [2]). Whenever it is feasible, there exists an integer solution x such that 0 ≤ x ij ≤ m which can be decomposed into m paths (not necessarily arc-disjoint) such that no tight arc appears more than once due to the constraints (20). This is exactly an mpath defined earlier.…”

Experimental evaluation of solution approaches for the K-route maximum flow problem

“…The MKRF problem, with K = 2, was originally formulated by Kishimoto and Takeuchi [3] and furtherly studied by Kishimoto et al [4].…”

“…In [5,6] a generalization to the K-route ows, for any value of K, has been considered, the theoretical properties of the problem have been investigated and an approach for its solution has been presented. In particular, an algorithm that solves the MKRF problem as a sequence of at most K maximum ow problems has been proposed in [6].…”

“…Some of the basic theory of [5,6] has been simpliÿed and extended by Aggarwal and Orlin [7], where two alternative solution approaches (i.e., the binary-search algorithm and the K-route ow algorithm) have been proposed.…”

Integer version of the multipath flow network synthesis problem

“…The following concept of multipath flows was introduced and studied by Kishimoto [20], Kishimoto and Takeuchi [21,22] and Kishimoto, Takeuchi and Kishi [23] for improving the reliability of communication networks where edges are subject to failure:…”