Efficient algorithms for network center/covering location optimization problems

We consider the algorithmic issues for the center and covering location optimization problems in network metric space. The demand set consists of all points of the network that require services and the supply set consists of all candidate locations of facilities in the underlying network. The center location problems aim to establish an optimal placement of facilities in the supply set in order to minimize the maximum distance from a demand point to its closest fac ility. The covering location problems seek to establish the minimum number of facilities such that the maximum distance from a demand point to its closest facility is no more than a predefined non-negative value. There is a tight relationship between the two problems. Generally, a solution for the covering location problem with a given value can be used to test the feasibility of the value in the corresponding center location problem. Four cases of the center problem and the corresponding covering problem, where the demand set and the supply set are either subsets of the vertex set or subsets of the point set of the underlying network, are considered. Moreover, when the demand set is a subset of the vertex set, its weighted version of the problem is considered where each demand vertex is associated with a non-negative weight. We study the center/covering location problems in general networks as well as specialized networks, such as tree networks, cactus networks, and partial k-tree networks for fixed k. We also look at some variations of the network center/covering location problem in an edge-weighted tree network, including conditional extensive facility location problems, continuous p-edge-partition problems, and constrained covering problems.