Securely Connected Facility Location in Metric Graphs

Connected facility location problems arise in many different applications areas, such as transportation, logistics, or telecommunications. Given a set of clients and potential facilities, one has to construct a connected facility network and attach the remaining clients to the chosen facilities via access links. Here, we consider interconnected facility location problems, where we request 1-or 2-connectivity in the subnetwork induced by the chosen facilities alone, disregarding client nodes. This type of connectivity is required in telecommunication networks, for example, where facilities represent core nodes that communicate directly with each other. We show that the interconnected facility location problem is strongly NP-hard for both 1and 2-connectivity among the facilities, even for metric edge costs. We present simple randomized approximation algorithms with expected approximation ratios 4.40 for 1-connectivity and 4.42 for 2-connectivity. For the classical 2-connected facility location problem, which allows to use non-facility nodes to connect facilities, we obtain an algorithm with expected approximation guarantee of 4.26.