Abstract
In this paper we present a new fast approximation algorithm for the Uniform Metric Labeling Problem. This is an important classification problem that occur in many applications which consider the assignment of objects into labels, in a way that is consistent with some observed data that includes the relationship between the objects.
The known approximation algorithms are based on solutions of large linear programs and are impractical for moderated and large size instances. We present an 8log n-approximation algorithm analyzed by a primal-dual technique which, although has factor greater than the previous algorithms, can be applied to large sized instances. We obtained experimental results on computational generated and image processing instances with the new algorithm and two others LP-based approximation algorithms. For these instances our algorithm present a considerable gain of computational time and the error ratio, when possible to compare, was less than 2% from the optimum.
This work has been partially supported by MCT/CNPq Project ProNEx grant 664107/97-4, FAPESP grants 01/12166-3, 02/05715-3, and CNPq grants 300301/98-7, 470608/01-3, 464114/00-4, and 478818/03-3.
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
Besag, J.: Spatial intteraction and the statistical analysis of lattice systems. J. Royal Statistical Society B 36 (1974)
Besag, J.: On the statistical analysis of dirty pictures. J. Royal Statistical Society B 48 (1986)
Chakrabarti, S., Dom, B., Indyk, P.: Enhanced hypertext categorization using hyperlinks. In: Proc. ACM SIGMOD (1998)
Chekuri, C., Khanna, S., Naor, J.S., Zosin, L.: Approximation algorithms for the metric labeling problem via a new linear programming formulation. In: Proc. of ACM-SIAM Symposium on Discrete Algorithms, pp. 109–118 (2001)
Chvátal, V.: A greedy heuristic for the set-covering problem. Math. of Oper. Res. 4(3), 233–235 (1979)
Cohen, F.S.: Markov random fields for image modeling and analysis. Modeling and Application of Stochastic Processes (1986)
Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM Journal on Computing 23(4), 864–894 (1994)
Dubes, R., Jain, A.: Random field models in image analysis. J. Applied Statistics 16 (1989)
Freivalds, K.: A nondifferentiable optimization approach to ratio-cut partitioning. In: Jansen, K., Margraf, M., Mastrolli, M., Rolim, J.D.P. (eds.) WEA 2003. LNCS, vol. 2647, Springer, Heidelberg (2003)
Gupta, A., Tardos, E.: Constant factor approximation algorithms for a class of classification problems. In: Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, pp. 125–131 (1998)
Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing lp. Journal of ACM, 795–824 (2003)
Kleinberg, J., Tardos, E.: Approximation algorithms for classification problems with pairwise relationships: Metric labeling and markov random fields. In: Proceedings of the 40th Annuall IEEE Symposium on Foundations of Computer Science, pp. 14–23 (1999)
Leighton, T., Rao, S.: Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. Journal of the ACM 46(6), 787–832 (1999)
Dash Optimization. Xpress-MP Manual. Release 13 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bracht, E.C., Meira, L.A.A., Miyazawa, F.K. (2004). A Greedy Approximation Algorithm for the Uniform Labeling Problem Analyzed by a Primal-Dual Technique. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-24838-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22067-1
Online ISBN: 978-3-540-24838-5
eBook Packages: Springer Book Archive