Polynomial-time Algorithm for Server Location Method for Keeping Small Distance from Clients to Servers During Failures

Large amount of contents in the Internet have increased loads of contents servers, networks and data centers, which may degrade quality of service. To solve this problem, there is a method that some mirror servers providing the same contents are located on a network and a request is navigated to one of the mirror servers. As the location of the mirror servers affects the quality of service, it is important to locate the mirror servers in the network so that a network should connect a user and one of mirror servers with small hop length after links fail. In this paper, we address the server location problem that determines the location of the servers satisfying the following constraint: any users can access servers within a small hop count even if some links fail. In the previous research, we proved that this problem is NP-hard and proposed some heuristic algorithms. In this paper, we present a polynomial-time algorithm when the number of simultaneously failed links is restricted to one and the increase of hop length is restricted, in other words, we can get the optimum solution of the optimization version to minimize the number of servers in polynomial time. Furthermore, we evaluate the performance of actual ISP network topologies by the algorithm from the viewpoint of the number of servers.