Optimization Problem for Network Design by Link Protection and Link Augmentation

Abstract

Information networks need high reliability. Although link failure is one of the causes of communication disconnection in networks, it is necessary to be able to continue communication even in such a failure. There are two approaches of link protection and link addition against link failure. Link protection is to make the failure probability of links sufficiently small by sufficient backup resource and rapid recovery system. Link addition is to increase network connectivity by adding new links to a network. Both link addition and link protection are methods to design a reliable network. Some network design methods either only by link addition or only by link protection have been investigated so far. However, it is possible to design a reliable network at lower cost by a combination of link addition and protection than a network designed either by only link addition or by only link protection. In this paper, we deal with a network design problem to realize a reliable network at lower cost by combining link addition and link protection. First, we formulate this network design problem as a decision problem and we prove the NP-hardness. Furthermore, we propose some polynomial-time algorithms for the problems of the optimization version under some restricted conditions.