Abstract
We apply and extend the priority algorithm framework introduced by Borodin, Nielsen and Rackoff to define “greedy-like” algorithms for (uncapacitated) facility location 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 definitions 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Borodin, M. Nielsen, and C. Rackoff. (Incremental) priority algorithms. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 752–761, 2002.
M. Charikar, C. Chekuri, T. Feder, and M. Motwani. Incremental clustering and dynamic information retrieval. In Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pages 626–634, 1997.
V. Chvátal. A greedy heuristic for the set covering problem. Mathematics of Operations Research, 4(3):233–235, 1979.
U. Feige. A threshold of ln n for approximating set cover. Journal of the ACM, 45(4):634–652, 1998.
S. Guha and S. Khuller. Greedy strikes back: Improved facility location algorithms. In Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, pages 649–657, 1998.
D. Hochbaum. Heuristics for the fixed cost median problem. Mathematical Programming, 22:148–162, 1982.
K. Jain, M. Mahdian, and A. Saberi. A new greedy approach for facility location problems. In Proceedings of the 34th Annual ACM Symposium on Theory of Computation, pages 731–740, 2002.
D.S. Johnson. Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences, 9(3):256–278, 1974.
L. Lovász. On the ratio of optimal integral and fractional covers. Discrete Mathematics, 13:383–390, 1975.
M. Mahdian, E. Markakis, A. Saberi, and V. V. Vazirani. A greedy facility location algorithm analyzed using dual fitting. In Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), pages 127–137, 2001.
M. Mahdian, J. Ye, and J. Zhang. A 1.52-approximation algorithm for the uncapacitated facility location problem. Available at http://www.mit.edu/~mahdian/pub.html.
R. R. Mettu and C. G. Plaxton. The online median problem. In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 339–348, 2000.
A. Meyerson. Online facility location. In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, pages 426–431, 2001.
D.B. Shmoys. Approximation algorithms for facility location problems. In K. Jansen and S. Khuller, editors, Approximation Algorithms for Combinatorial Optimization, volume 1913 of Lecture Notes in Computer Science. Springer, Berlin, 2000.
D.B. Shmoys, E. Tardos, and K. Aardal. Approximation algorithms for facility location problems (extended abstract). In Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pages 265–274, 1997.
P. Slavík. A tight analysis of the greedy algorithm for set cover. Journal of Algorithms, 25:237–254, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Angelopoulos, S., Borodin, A. (2002). On the Power of Priority Algorithms for Facility Location and Set Cover. In: Jansen, K., Leonardi, S., Vazirani, V. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2002. Lecture Notes in Computer Science, vol 2462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45753-4_5
Download citation
DOI: https://doi.org/10.1007/3-540-45753-4_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44186-1
Online ISBN: 978-3-540-45753-4
eBook Packages: Springer Book Archive