On the Power of Priority Algorithms for Facility Location and Set Cover

We apply and extend the priority algorithm framework introduced by Borodin, Nielsen and Rackoo to deene \greedy-like" algorithms for (uncapacitated) facility location problems and set cover. These problems have been the focus of extensive research from the point of view of approximation algorithms, and for both problems, greedy algorithms have been proposed and analyzed. The priority algorithm deenitions are general enough so as to capture a broad class of algorithms that can be characterized as \greedy-like" while still possible to derive non-trivial lower bounds on the approximability of the problems. Our results are orthogonal to complexity considerations, and hence apply to algorithms that are not necessarily polynomial-time.