Detecting Critical Links for Keeping Shortest Distance from Clients to Servers during Failures

Recently, large-volume contents distributed by a content delivery service~(CDS) on the Internet increase load of content delivery servers and networks, which is at the risk for degradation of quality of service. To overcome this problem, some mirror servers providing the same content are located on a network, and a request is navigated to one of the mirror servers. A reliable CDS must offer connectivity between a user and servers with small hop count even during link failure. Therefore, the introduction of mirror servers causes a new problem such as a high reliable network design which is appropriate for CDS. In this paper, we address a reliable network design problem by protection of critical links whose failures significantly degrade performance. The objective is to find the smallest number of the links to be protected so that all users can access servers within a small hop count even if non-protected links fail. First, we formulate this problem and prove that it is NP-hard. Second, we make clear the conditions that the problem is solvable in polynomial time. Specifically, we present a polynomial-time algorithm to solve the problem when the number of simultaneously failed link is restricted to one. Furthermore, we show that the problem can be solved also in polynomial time when hop count is restricted to one.