Minimum cost paths subject to minimum vulnerability for reliable communications

In real networks, disjoint paths are needed for providing protection against single link/node failure. When disjoint paths cannot be found, an alternative solution is to find paths with the minimum shared links/nodes. In the literature, there is little work addressing this problem. In this paper, defining vulnerability as the number of times a link/node is shared among different paths, we consider the problems of finding k paths with minimum edge/node vulnerability. We study three problems and propose polynomial algorithms to solve these problems. The work presented in this paper can be directly applied to a number of network applications such as reliable unicast/multicast communications, reliable client-server communications, protection for the dual-homing architecture, etc.