The power of priority algorithms for facility location and set cover (Q1884771)

\textit{A. Borodin, M. N. Nielsen} and \textit{C. Rackoff} [Algorithmica 37, 295--326 (2003; Zbl 1082.68521)] introduced the class of so-called priority algorithms as a model for describing natural greedy-like algorithms. In this paper the framework is followed to characterize greedy and greedy-like algorithms for the uncapacitated facility location problem and the set cover problem. The authors give several approximability results. For example, Theorem 1 says that no priority algorithm for the uniform metric facility location problem can achieve an approximation ratio better than 4/3 and by Theorem 8 no priority algorithm for set cover performs better than the greedy algorithm.