A linear programming formulation and approximation algorithms for the metric labeling problem

SIAM Journal on Discrete Mathematics

Volumn 18, Issue 3, 2004, Pages 608-625

  Chekuri, C ^a   Khanna, S ^b   Naor, J ^c   Zosin, L ^d  

^a LUCENT TECHNOLOGIES   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^d Bear Stearns & Co Inc   (United States)

Author keywords

Approximation algorithm; Linear program; Metric labeling; Truncated linear metric

Indexed keywords

APPROXIMATION ALGORITHMS; LINEAR PROGRAM; METRIC LABELING; TRUNCATED LINEAR METRIC;

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER VISION; INTEGER PROGRAMMING; PROBLEM SOLVING; THEOREM PROVING;

LINEAR PROGRAMMING;

EID: 23844432639     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480101396937     Document Type: Article

References (33)

1. A. ARCHER, J. FAKCHAROENPHOL, C. HARRELSON, R. KRAUTHGAMER, K. TALWAR, AND É. TARDOS, Approximate classification via earthmover metrics, in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, 2004, pp. 1072-1080.
2. Y. BARTAL, Probabilistic approximation of metric spaces and its algorithmic applications, in Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science, 1996, pp. 184-193.
3. Y. BARTAL, On approximating arbitrary metrics by tree metrics, in Proceedings of the 30th Annual ACM Symposium on Theory of Computing, 1998, pp. 161-168.
4. Y. BOYKOV, O. VEKSLER, AND R. ZABIH, Markov random fields with efficient approximations, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 1998, pp. 648-655.
5. Y. BOYKOV, O. VEKSLER, AND R. ZABIH, Fast approximate energy minimization via graph cuts, in Proceedings of the 7th IEEE International Conference on Computer Vision, 1999, pp. 377-384.
6. Y. BOYKOV, O. VEKSLER, AND R. ZABIH, A new algorithm for energy minimization with discontinuities, in Proceedings of the International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, 1999.
7. G. CǍLINESCU, H. KARLOFF, AND Y. RABANI, An improved approximation algorithm for multiway cut, J. Comput. System Sci., 60 (2000), pp. 564-574.
8. G. CALINESCU, H. KARLOFF, AND Y. RABANI, Approximation algorithms for the 0-extension problem, SIAM J. Comput., 34 (2004), pp. 358-372.
9. M. CHARIKAR, C. CHEKURI, A. GOEL, AND S. GUHA, Rounding via trees: Deterministic approximation algorithms for group steiner trees and k-median, in Proceedings of the 30th ACM Symposium on Theory of Computing, 1998, pp. 114-123.
10. J. CHUZHOY, private communication, 2001.
11. J. CHUZHOY AND J. NAOR, The hardness of metric labeling, in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, 2004, pp. 108-114.
12. F. S. COHEN, Modeling and applications of stochastic processes, in The Markov Random Fields for Image Modeling and Analysis, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1986, pp. 243-272.
13. E. DALHAUS, D. S. JOHNSON, C. H. PAPADIMITRIOU, P. D. SEYMOUR, AND M. YANNAKAKIS, The complexity of multiterminal cuts, SIAM J. Comput., 23 (1994), pp. 864-894.
14. R. DUBES AND A. JAIN, Random field models in image analysis, J. Appl. Stat., 16 (1989), pp. 131-164.
15. J. FAKCHAROENPHOL, C. HARRELSON, S. RAO, AND K. TALWAR, An improved approximation algorithm for the 0-extension problem, in Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, 2003, pp. 257-265.
16. J. FAKCHAROENPHOL, S. RAO, AND K. TALWAR, A tight bound on approximating arbitrary metrics by tree metrics, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing, 2003, pp. 448-455.
17. D. GREIG, B. PORTEOUS, AND A. SEHEULT, Exact maximum a posteriori estimation for binary images, J. Roy. Statist. Soc. Ser. B, 51 (1989), pp. 271-279.
18. A. GUPTA AND E. TARDOS, Constant factor approximation algorithms for a class of classification problems, in Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, 2000, pp. 652-658.
19. D. HOCHBAUM, An efficient algorithm for image segmentation, markov random fields and related problems, J. ACM, 48 (2001), pp. 686-701.
20. A. J. HOFFMAN, On simple linear programming problems, in Proceedings of the 7th Symposium in Pure Mathematics, Vol. 7, V. Klee, ed., AMS, Providence, RI, 1963, pp. 317-327.
21. H. ISHIKAWA AND D. GEIGER, Segmentation by grouping junctions, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 1998, pp. 125-131.
22. H. ISHIKAWA AND D. GEIGER, Mapping image restoration to a graph problem, in Proceedings of the 1999 IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, 1999.
23. D. KARGER, P. KLEIN, C. STEIN, M. THORUP, AND N. YOUNG, Rounding algorithms for a geometric embedding of multiway cut, in Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, 1999, pp. 668-678.
24. A. KARZANOV, Minimum 0-extension of graph, metrics, European J. Combin., 19 (1998), pp. 71-101.
25. A. KARZANOV, A combinatorial algorithm for the minimum (2,r)-metric problem and some generalizations, Combinatorica, 18 (1999), pp. 549-569.
26. J. KLEINBERG AND E. TARDOS, Approximation algorithms for classification problems with pair-wise relationships: Metric labeling and markov random fields, J. ACM, 49 (2002), pp. 616-630.
27. S. Z. LI, Markov Random Field Modeling in Computer Vision, 2nd ed., Springer-Verlag, New York, 2001.
28. I. MILIS, Task assignment in distributed systems using network flow methods, in Proceedings of the Conference on Combinatorics and Computer Science, Lecture Notes in Comput. Sci. 1120, Springer-Verlag, Berlin, 1996, pp. 396-405.
29. G. MONGE, Déblai et Ramblai, Mem. de l'Academie des Sciences, 1781.
30. S. PELEG, M. WERMAN, AND H. ROM, A unified approach to the change of resolution: Space and gray-level, IEEE Trans. Pattern Anal. Machine Intel., 11 (1989), pp. 739-742.
31. S. RACHEV, The Monge-Kantorovich mass transference problem and its stochastic applications, Theory Probab. Appl., 29 (1984), pp. 647-676.
32. S. ROY AND I. Cox., A maximum-flow formulation of the N-camera stereo correspondence problem, in Proceedings of the International Conference on Computer Vision, 1998, pp. 492-499.
33. Y. RUBNER, C. TOMASI, AND L. GUIBAS, The earth mover's distance as a metric for image retrieval, Int. J. Comput. Vis., 40 (2000), pp. 99-121.