Edge-disjoint paths in planar graphs

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2004, Pages 71-80

  Chekuri, C ^a   Khanna, S ^b   Shepherd, F B ^a  

^a LUCENT TECHNOLOGIES   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EDGE-DISJOINT PATHS; HIGH-SPEED NETWORKS; PLANAR GRAPHS; VIRTUAL CIRCUIT ROUTING;

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SCIENCE; COMPUTER TERMINALS; INTERFACES (COMPUTER); OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

GRAPH THEORY;

EID: 17744391610     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (41)

1. Y. Aumann and Y. Rabani. Improved Bounds for All Optical Routing. SODA 1995, pp. 567-576.
2. Y. Aumann and Y. Rabani. An O(log k) approximate mincut max-flow theorem and approximation algorithm. SIAM Journal on Computing, 27(1):291-301, February 1998.
3. A. Baveja and A. Srinivasan. Approximation algorithms for disjoint paths and related routing and packing problems. Mathematics of Operations Research, Vol. 25, pp. 255-280, 2000.
4. C. Chekuri, S. Khanna, and F. B. Shepherd. The All-or-Nothing Multi-commodity Flow Problem. Proc. of STOC, June 2004.
5. C. Chekuri, S. Khanna, and F. B. Shepherd. A deletable edge lemma for general graphs. Manuscript, 2004.
6. C. Chekuri and S. Khanna. On Multidimensional Packing Problems. SIAM J. on Computing, 33(4):837-851, 2004. Preliminary version in Proc. of SODA, 1999.
7. C. Chekuri and S. Khanna. On Multidimensional Packing Problems. SIAM J. on Computing, 33(4):837-851, 2004. Preliminary version in Proc. of SODA, 1999.
8. C. Chekuri and S. Khanna. Edge Disjoint Paths Revisited. Proc. of SODA, 2003.
9. C. Chekuri, M. Mydlarz, and F. B. Shepherd. Multicommodity Demand Flow in a Tree and Packing Integer Programs. Submitted. Preliminary version in Proc. of ICALP, 2003.
10. J. Chuzhoy and J. Naor. New inapproximability results for congestion minimization and machine scheduling. Proc. of STOC, 2004.
11. S. Even, A. Itai and A. Shamir. On the complexity of timetable and multicommodity flow problems. SIAM J. on Computing, Vol 5, 691-703, 1976.
12. J. Fakcheroenphol and K. Talwar. An Improved Decomposition Theorem for Graphs Excluding a Fixed Minor. Proc. of APPROX, 2003.
13. A. Frank. Edge-disjoint paths in planar graphs. J. of Combinatorial Theory, Ser. B., No. 2 (1985), 164-178.
14. A. Frank. Packing paths, cuts, and circuits - a survey. In B. Korte, L. Lovász, H. J. Prömel, and A. Schrijver, eds., Paths, Flows and VLSI-Layout, 49-100. Springer Verlag, Berlin, 1990.
15. S. Fortune, J. Hopcroft and J. Wyllie. The directed subgraph homeomorphism problem. Theoretical Computer Science, 10(2):111-121, 1980.
16. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, 1979.
17. N. Garg, V. Vazirani, M. Yannakakis. Primal-Dual Approximation Algorithms for Integral Flow and Multicut in Trees. Algorithmica, 18(1):3-20, 1997.
18. V. Guruswami, S. Khanna, R. Rajaraman, F. B. Shepherd, and M. Yannakakis. Near-Optimal Hardness Results and Approximation Algorithms for Edge-Disjoint Paths and Related Problems. JCSS, 67:473-496, 2003.
19. C. Harrelson, K. Hildrum, and S. Rao. A polynomial-time tree decomposition to minimize congestion. Proc. of SPAA, 2003.
20. R. M. Karp. Reducibility among combinatorial problems. Complexity of Computer Computations, R. E. Miller, J. W. Thatcher, Eds., New York: Plenum Press, 1972, 85-103.
21. J. M. Kleinberg and E. Tardos. Approximations for the disjoint paths problem in high-diameter planar networks. Journal of Computer and System Sciences, 57:61-73, 1998.
22. J. M. Kleinberg and É. Tardos. Disjoint Paths in Densely Embedded Graphs. Proc. of FOCS, pp. 52-61, 1995.
23. P. Klein, S. Plotkin and S. Rao. Planar graphs, multicommodity flow, and network decomposition. Proc. of STOC, 1993.
24. J. M. Kleinberg. Approximation algorithms for disjoint paths problems. PhD thesis, MIT, Cambridge, MA, 1996.
25. J. M. Kleinberg. Decision algorithms for unsplittable flow and the half-disjoint paths problem. Proc. of STOC, pp. 530-539, 1998.
26. S. G. Kolliopoulos and C. Stein. Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs. Proc. of IPCO, 1998.
27. P. Kolman and S. Scheideier. Improved bounds for the unsplittable flow problem. In Proc. of SODA, 2002.
28. M. R. Kramer and J. L. van Leeuwen. The complexity of wire-routing and finding minimum area layouts for arbitrary VLSI circuits. VLSI-Theory (F. P. Preparata ed.) [Advances in Computing Research, Volume 2], JAI Press, Greenwich, Connecticut, 1984, 129-146.
29. T. Leighton and S. Rao. Multicommodity max-flow mincut theorems and their use in designing approximation algorithms. JACM, 46(6):787-832, 1999.
30. N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Combinatorica, 15(2):215-245, 1995.
31. J. F. Lynch. The equivalence of theorem proving and the interconnection problem. ACM SIGDA Newsletter, 5:3, 1975.
32. H. Okamura and P.D. Seymour. Multicommodity flows in planar graphs. Journal of Combinatorial Theory, Series B, 31 (1981) 75-81.
33. H. Räcke. Minimizing congestion in general networks. Proc. of FOCS, 2002.
34. P. Raghavan and C. D. Thompson. Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica, 7:365-374, 1987.
35. N. Robertson and P. D. Seymour. Outline of a disjoint paths algorithm. In B. Korte, L. Lovász, H. J. Prömel, and A. Schrijver, Eds., Paths, Flows and VLSI-Layout. Springer-Verlag, Berlin, 1990.
36. N. Robertson, P. D. Seymour and R. Thomas. Quickly Excluding a Planar Graph. Journal of Combinatorial Theory (B), 62: 323-348 (1994).
37. N. Robertson and P. D. Seymour. Graph Minors X. Obstructions to Tree-Decomposition. Journal of Combinatorial Theory (B), 52: 153-190 (1991).
38. P. D. Seymour and R. Thomas. Call Routing and the Ratcatcher. Combinatorica, 14(2): 217-241 (1994).
39. A. Schrijver. Combinatorial Optimization: Polyhedra and Efficieny. Springer-Verlag, Berlin Hiedelberg, 2003.
40. A. Srinivasan. Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems. Proc. of the FOCS, pp. 416-425, 1997.
41. K. Varadarajan and G. Venkataraman. Graph Decomposition and a Greedy Algorithm for Edge-disjoint Paths. Proc. of SODA, 2004.