On multipath routing using widest pair of disjoint paths

Multipath and disjoint path routing schemes have received a considerable amount of attention in the networking research community in recent years due to many of advantages offered by such schemes. Delay, delay-jitter, bandwidth, are often used as parameters to specify quality-of-service. One of the most important parameters is the bandwidth of the route used for data transmission. A path from a source node s to a destination node t is known as the widest path if the bandwidth of this path is the largest among all paths between s to t. Algorithms for computing a widest path between a source-destination node pair is well-known. In this paper, we consider two problems where the notions of multipath, disjoint path and widest path are combined. In one version, we address the problem of finding a pair of disjoint paths between a source-destination node pair, such that the combined bandwidth of this path-pair is the maximum over all such pairs. In the other version, we want to find a pair of disjoint paths, such that the bandwidth of the first path is at least X₁ and the bandwidth of the second path is at least X₂, for some pre-specified values X₁ and X₂. We prove that both versions of the problem are NP-complete. We provide exact and approximate solutions for both versions of the problem. We show that our approximate solutions provide near-optimal solutions for almost all the instances of the problem.