Maximum-Bandwidth Node-Disjoint Paths

Abstract

This paper presents a new method for finding the node-disjoint paths with maximum combined bandwidth in communication networks. This problem is an NP-complete problem which can be optimally solved in exponential time using integer linear programming (ILP). The presented method uses a maximum-cost variant of Dijkstra algorithm and a virtual-node representation to obtain the maximum-bandwidth node-disjoint path. Through several simulations, we compare the performance of our method to a modern heuristic technique and to the ILP solution. We show that, in a polynomial execution time, our proposed method produces results that are almost identical to ILP in a significantly lower execution time. In this paper, our focus is on the problem of finding two node-disjoint paths such that the bandwidth sum of the two paths is the maximum possible two-disjoint-paths sum between a given source and destination nodes in the network. This is essentially an MCP problem with two constraints: The first constraint is for the two paths to be node-disjoint. The second constraint is maximizing the bandwidth sum of the two paths. This is also an NP-complete problem as shown in (9). We develop a near-optimal method for solving this problem in polynomial time. The proposed method uses a virtual-node representation from the original network. We implement a variant of Dijkstra algorithm that finds the optimal path based on the maximum bandwidth (10). The variant algorithm is further modified to work concurrently on two paths, avoiding nodes that lead to overlapped paths in the original network. The algorithm is then applied iteratively to obtain the maximum disjoint path in the actual network. In the remaining part of the paper, we discuss related studies that attempted to find solutions to the maximum-pair disjoint paths and similar problems. Next, we illustrate the modified Dijkstra algorithm that finds the maximum- bandwidth path. The new method is then presented in details and demonstrated by an example. The performance of our method is evaluated and compared to a modern heuristic algorithm and to the exact solution using ILP. Analytical study of the presented method is then presented to show the order of its execution time. The paper is concluded with a summary and future work.