A Greedy Approximation Algorithm For The Uniform Labeling Problem Analyzed By A Primal-dual Technique

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 8 log 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. © Springer-Verlag 2004.3059145158Besag, J., Spatial intteraction and the statistical analysis of lattice systems (1974) J. Royal Statistical Society B, 36Besag, J., On the statistical analysis of dirty pictures (1986) J. Royal Statistical Society B, 48Chakrabarti, S., Dom, B., Indyk, P., Enhanced hypertext categorization using hyperlinks (1998) Proc. ACM SIGMODChekuri, C., Khanna, S., Naor, J.S., Zosin, L., Approximation algorithms for the metric labeling problem via a new linear programming formulation (2001) Proc. of ACM-SIAM Symposium on Discrete Algorithms, pp. 109-118Chvátal, V., A greedy heuristic for the set-covering problem (1979) Math, of Oper. Res., 4 (3), pp. 233-235Cohen, F.S., Markov random fields for image modeling and analysis (1986) Modeling and Application of Stochastic ProcessesDahinaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M., The complexity of multiterminal cuts (1994) SIAM Journal on Computing, 23 (4), pp. 864-894Dubes, R., Jain, A., Random field models in image analysis (1989) J. Applied Statistics, 16Freivalds, K., A nondifferentiable optimization approach to ratio-cut partitioning (2003) Proc. 2nd Workshop on Efficient and Experimental Algorithms, , Lectures Notes on Computer Science, LNCS 2647. Springer-VerlagGupta, A., Tardos, E., Constant factor approximation algorithms for a class of classification problems (1998) Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, pp. 125-131Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V., Greedy facility location algorithms analyzed using dual fitting with factor-revealing Ip (2003) Journal of ACM, pp. 795-824Kleinberg, J., Tardos, E., Approximation algorithms for classification problems with pairwise relationships: Metric labeling and markov random fields (1999) Proceedings of the 40th Annuall IEEE Symposium on Foundations of Computer Science, pp. 14-23Leighton, T., Rao, S., Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms (1999) Journal of the ACM, 46 (6), pp. 787-832. , NovDash Optimization (2002) Xpress-MP Manual. Release 1