Geometry helps in bottleneck matching and related problems

Algorithmica (New York)

Volumn 31, Issue 1, 2001, Pages 1-28

  Efrat, A ^a   Itai, A ^b   Katz, M J ^c  

^a TEL AVIV UNIVERSITY   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Approximation; Bipartite graph matching; Bottleneck matching; Euclidean distance; Minkowski norm; Translation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; GRAPH THEORY; PATTERN RECOGNITION; SET THEORY;

BOTTLENECK MATCHING;

PROBLEM SOLVING;

EID: 0242333224     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-001-0016-8     Document Type: Article

References (46)

1. P.K. Agarwal, B. Aronov, M. Sharir and S. Suri, Selecting distances in the plane, Algorithmica 9 (1993), 495-514.
2. P.K. Agarwal, A. Efrat and M. Sharir, Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications, Proceedings of the 11th Annual Symposium on Computational Geometry, 1995, pp. 39-50.
3. M. Ajtai, J. Komlós and E. Szemerédi, Sorting in c log n parallel steps, Combinatorica 3 (1983), 1-19.
4. H. Alt, B. Behrends, and J. Blömer, Approximate matching of polygonal shapes. Proceedings of the 7th Annual Symposium on Computational Geometry, 1991, pp. 186-193.
5. H. Alt, K. Mehlhorn, H. Wagener and E. Welzl, Congruence, similarity and symmetries of geometric objects, Discrete Comput. Geom. 3 (1988), 237-256.
6. E.M. Arkin, K. Kedem, J.S.B. Mitchell, J. Sprinzak and M. Werman, Matching points into noise regions: combinatorial bounds and algorithms, Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, 1991, pp. 42-51.
7. S. Arya, D.M. Mount, N.S. Netanyahu, R. Silverman and A. Wu, An optimal algorithm for approximate nearest neighbor searching, Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, 1994, pp. 573-582.
8. M. de Berg, M. van Krevekd, M. Overmars and O. Schwarzkopf, Computational Geometry, Algorithms and Applications, Springer-Verlag, New York, 1997.
9. C. Berge, Two theorems in graph theory, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 842-844.
10. S.N. Bespamyatnikh. Dynamic algorithms for approximate neighbor searching. Proceedings of the 8th Candian Conference on Computational Geometry, 1996, pp. 252-257.
11. S. Buss and P. Yianilos, Linear and O(n log n) time minimum-cost matching algorithms for quasi-convex tours, Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, 1994, pp. 65-76.
12. L.P. Chew, D. Dor, A. Efrat and K. Kedem, Geometric pattern matching in d-dimensional space, Proceedings of the Third European Symposium on Algorithms (ESA), LNCS Vol. 979, Springer-Verlag, Berlin, 1995, pp. 264-279.
13. L.P. Chew, M.T. Goodrich, D.P. Huttenlocher, K. Kedem, J.M. Kleinberg and D. Kravets, Geometric pattern matching under Euclidean motion, Proceedings of the 5th Candian Conference on Computational Geometry, 1993, pp. 151-156.
14. L.P. Chew and K. Kedem, Improvements on geometric pattern matching problems, Proceedings of the 3rd Scandinavian Workshop on Algorithms Theory, LNCS Vol. 621, Springer-Verlag, Berlin, 1992, pp. 318-325.
15. R. Cole, Slowing down sorting networks to obtain faster sorting algorithms, J. Assoc. Comput. Mach. 34 (1987), pp. 200-208.
16. E.A. Dinitz, Algorithm for solution of a problem of maximum flow in a network with power estimation, Soviet Math. Dokl. 11, (1970), pp. 248-264.
17. H. Edelsbrunner, L. Guibas and J. Stolfi, Optimal point location in a monotone subdivision, SIAM J. Comput. 15 (1986), pp. 317-340.
18. J. Edmonds and R.M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, J. Assoc. Comput. Mach. 19 (1972), pp. 248-264.
19. A. Efrat, Finding approximate matching of points under translation, Manuscript, 1995.
20. A. Efrat, Geometric Location Optimization, Ph.D. Dissertion, Tel-Aviv University, 1998.
21. A. Efrat and A. Itai, Improvements on bottleneck matching and related problems using geometry, Proceedings of the 12th Annual Symposium on Computational Geometry, 1996, pp. 301-310.
22. A. Efrat and M.J. Katz, Computing fair and bottleneck matchings in geometric graphs, Proceedings of the 7th International Symposium on Algorithms and Computation (ISAAC), 1996, pp. 115-125.
23. A. Efrat, M.J. Katz, F. Nielsen, and M. Sharir, Dynamic data structures for fat objects and their applications, Proceedings of the 5th Workshop on Algorithms and Data Structures, LNCS Vol. 1272, Springer-Verlag, Berlin, 1997, pp. 297-306.
24. A. Efrat, M. Sharir and A. Ziv, Computing the smallest k-enclosing circle and related problems, Comput. Geom Theory Appl. 4 (1995), pp. 119-136.
25. G.N. Frederickson and D.B. Johnson, Generalized selection and ranking sorted matrices, SIAM J. Comput. 13 (1984), pp. 14-30.
26. S.K. Gupta and A.P. Punnen, Minimum deviation problems, Oper. Res. Lett. 7 (1988), pp. 201-204.
27. D. Halperin and M. Sharir, New bounds for lower envelopes in three dimensions, with applications to visibility of terrains, Discrete Comput. Geom. 12 (1994), pp. 313-326.
28. P.J. Heffeman, Generalized approximate algorithms for point set congruence, Proceedings of the 3rd Workshop on Algorithms and Data Structures, LNCS Vol. 709, Springer-Verlag, Berlin, 1993, pp. 373-384.
29. P.J. Heffernan and S. Schirra, Approximate decision algorithms for point set congruence, SIAM J. Comput. 8 (1992), pp. 93-101.
30. J. Hershberger and S. Suri, Applications of a semi-dynamic convex hull algorithm, Proceedings of the 2nd Scandinavian Workshop on Algorithms Theory, LNCS Vol. 447, Springer-Verlag, Berlin, 1990, pp. 380-392.
31. J. Hershberger and S. Suri, Finding tailored partitions, J. Algorithms 12 (1991), 431-463.
32. 5/2 algorithm for maximum matchings in bipartite graphs, SIAM J. Comput. 2 (1973), 225-231.
33. D.P. Huttenlocher and K. Kedem, Efficiently computing the Hausdorff distance for point sets under translation, Proceedings of the 6th Annual Symposium on Computational Geometry, 1990, pp. 340-349.
34. D.P. Huttenlocher, K. Kedem and M. Sharir, The upper envelope of Voronoi surfaces and its applications, Discrete Comput. Geom. 9 (1993), pp. 267-291.
35. P. Indyk and S. Venkatasubramanian, Approximate congruence in nearly linear time, Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, 2000, pp. 354-360.
36. A.V. Karzanov, Exact complexity bound for a max-flow algorithm applied to "representatives" problem, Voprosy Kibernetiki (Proceedings of the Seminar on Combinatorial Mathematics, Moscow, January 1971). Akad. Nauk SSSR, Scientific Council on the Complex Problem "Kibernetika," 1973, pp. 66-70 (in Russian).
37. M.J. Katz and M. Sharir, An expander-based approach to geometric optimization, SIAM J. Comput. 26 (1997), 1384-1408.
38. H. Kuhn, The Hungarian method for the assignment problem, Naval Res. Logist. Quart. 2 (1955), pp. 83-97.
39. E. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, 1976.
40. L. Lovasz and M.D. Plummer, Matching Theory, Annals of Discrete Mathematics, Vol. 29, North-Holland, Amsterdam, 1986.
41. S. Martello, W.R. Pulleyblank, P. Toth and D. de Werra, Balanced optimization problems, Oper. Res. Lett. 3 (1984), 275-278.
42. N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, J. Assoc. Comput. Mach. 30 (1983), 852-865.
43. M.H. Overmars and J. van Leeuwen, Maintenance of configurations in the plane, J. Comput. System Sci. 23 (1981), 166-204.
44. M. Sharir, A near-linear algorithm for the planar 2-center problem, Discrete Comput. Geom. 18 (1997), 125-134.
45. R.E. Tarjan, Data Structures and Network Algorithms, SIAM, Philadelphia, PA, 1983.
46. P.M. Vaidya, Geometry helps in matching, SIAM J. Comput. 18 (1989), 1201-1225.