Abstract
We continue the study of priority or “greedy-like” algorithms as initiated in [6] and as extended to graph theoretic problems in [9]. Graph theoretic problems pose some modelling problems that did not exist in the original applications of [6] and [2]. Following [9], we further clarify these concepts. In the graph theoretic setting there are several natural input formulations for a given problem and we show that priority algorithm bounds in general depend on the input formulation. We study a variety of graph problems in the context of arbitrary and restricted priority models corresponding to known “greedy algorithms”.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Angelopoulos, S.: Order-preserving transformations and greedy-like algorithms. In: Persiano, G., Solis-Oba, R. (eds.) WAOA 2004. LNCS, vol. 3351, pp. 197–210. Springer, Heidelberg (2005)
Angelopoulos, S., Borodin, A.: On the power of priority algorithms for facility location and set cover. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 26–39. Springer, Heidelberg (2002)
Bellare, M., Goldreich, O., Sudan, M.: Free bits, PCPs and non-approximability—towards tight results. SIAM Journal on Computing 27, 804–915 (1998)
Berman, P., Fujito, T.: On approximation properties of the independent set problem for degree 3 graphs. In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 449–460. Springer, Heidelberg (1995)
Boppana, R., Halldórsson, M.M.: Approximating maximum independent sets by excluding subgraphs. Bit 32, 180–196 (1992)
Borodin, A., Nielsen, M., Rackoff, C.: (Incremental) priority algorithms. Algorithmica 37, 295–326 (2003)
Borodin, A., Boyar, J., Larsen, K.S.: Priority algorithms for graph optimization problems. Preprint PP-2004-10, Department of Mathematics and Computer Science, University of Southern Denmark (2004)
Clarkson, K.L.: A modification of the greedy algorithm for vertex cover. Information Processing Letters 16, 23–25 (1983)
Davis, S., Impagliazzo, R.: Models of greedy algorithms for graph problems. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (2004)
Dinur, I., Safra, S.: The importance of being biased. In: Proceedings of the 34th Symposium on Theory of Computing, pp. 33–42. ACM Press, New York (2002)
Edmonds, J.: Matroids and the greedy algorithm. Mathematical Programming 1, 127–136 (1971)
Feige, U., Kilian, J.: Zero knowledge and the chromatic number. Journal of Computer and System Sciences 57, 187–199 (1998)
Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta Mathematica 182, 105–142 (1999)
Halldórsson, M.M.: A still better performance guarantee for approximate graph coloring. Information Processing Letters 45, 19–23 (1993)
Hochbaum, D.: Efficient bounds for the stable set, vertex cover and set packing problems. Discrete Applied Mathematics 6, 243–254 (1983)
Johnson, D.S.: Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9(3), 256–278 (1974)
Khanna, S., Linial, N., Safra, S.: On the hardness of approximating the chromatic number. Combinatorica 20(3), 393–415 (2000)
Lehmann, D., O’Callaghan, L., Shoham, Y.: Truth revelation in approximately efficient combinatorial auctions. Journal of the ACM 49(5), 1–26 (2002)
Papadimitriou, C., Yannakakis, M.: Optimization, approximation and complexity classes. Journal of Computer and System Sciences 43, 425–440 (1991)
Szekeres, G., Wilf, H.S.: An inequality for the chromatic number of graphs. Journal of Combinatorial Theory 4, 1–3 (1968)
Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borodin, A., Boyar, J., Larsen, K.S. (2005). Priority Algorithms for Graph Optimization Problems. In: Persiano, G., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2004. Lecture Notes in Computer Science, vol 3351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31833-0_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-31833-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24574-2
Online ISBN: 978-3-540-31833-0
eBook Packages: Computer ScienceComputer Science (R0)