On multipath routing using widest pair of disjoint paths

Multipatb and disjoint path routing schemes have received 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 parameter 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 X ₁ and the bandwidth of the second path is at least X ₂, for some pre-specified values X ₁ and X ₂. 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.