On the stable set polytope of a series-parallel graph
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the facets of the simple plant location packing polytope
Discrete Applied Mathematics - Workshop on discrete optimization DO'99, contributions to discrete optimization
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
SIAM Journal on Computing
On the Integrality of Some Facility Location Polytopes
SIAM Journal on Discrete Mathematics
The approximation gap for the metric facility location problem is not yet closed
Operations Research Letters
A family of facets for the uncapacitated p-median polytope
Operations Research Letters
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We study a prize-collecting version of the uncapacitated facility location problem and of the $p$-median problem. We say that the uncapacitated facility location polytope has the intersection property if adding the extra equation that fixes the number of opened facilities does not create any fractional extreme point. We characterize the graphs for which this polytope has the intersection property and give a complete description of the polytope for this class of graphs. This characterization yields a polynomial time cutting plane algorithm for these graphs. We also give a combinatorial polynomial time algorithm to solve the different variants of the $p$-median and facility location problems studied in this paper.