Finding minimum-cost paths with minimum sharability

In communication networks, multiple communication paths sharing minimum number of links or/and nodes may be desirable for improved performance, resource utilization and reliability. We introduce the notion of link sharability and node sharability, and consider the problems of finding minimum-cost k paths subject to minimum link/node sharability constraints. We identify 65 different link/node sharability constraints, and consider the fundamental problem of finding minimum-cost k paths between a pair of nodes under these constraints. We present a unified polynomial-time algorithm scheme for solving this problem subject to 25 of these different sharability constraints.