One-way and round-trip center location problems

Since the classical p-center problem is NP-hard, so are the one-way and the round-trip models we study. We present efficient constant factor approximation algorithms for these problems on general networks. Turning to special networks, we prove that the one-way problem is strongly NP-hard even on path networks. We then present polynomial time algorithms for the round-trip problem on general tree networks. We also discuss the single center case, and provide polynomial time algorithms for general networks, tree networks and planar Euclidean and rectilinear metric spaces.