The disjoint paths problem: Algorithm and structure

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6552 LNCS, Issue , 2011, Pages 2-7

  Kawarabayashi, Ken Ichi ^a  

^a NATIONAL INSTITUTE OF INFORMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CENTRAL PROBLEMS; DISJOINT PATHS; DISJOINT PATHS PROBLEM; GRAPH G; HIGH-SPEED; TECHNICAL PROBLEM; TRANSPORTATION NETWORK; VERTEX DISJOINT PATHS; VIRTUAL CIRCUIT ROUTING; VLSI LAYOUT;

ALGORITHMS; COMBINATORIAL OPTIMIZATION; HIGH SPEED NETWORKS; TREES (MATHEMATICS);

GRAPH THEORY;

EID: 79952274065     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-19094-0_2     Document Type: Conference Paper

References (35)

1. Andrews, M.: Approximation algorithms for the edge-disjoint paths problem via Räcke decompositions. In: Proc. 51st IEEE Symposium on Foundations of Computer Science, FOCS (2010)
2. Andrews, M., Zhang, L.: Hardness of the undirected edge-disjoint paths problem. In: Proc. 37th ACM Symposium on Theory of Computing (STOC), pp. 276-283 (2005)
3. Andrews, M., Chuzhoy, J., Khanna, S., Zhang, L.: Hardness of the undirected edge-disjoint paths problem with congestion. In: Proc. 46th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 226-244 (2005)
4. Bollobás, B., Thomason, A.: Highly linked graphs. Combinatorica 16, 313-320 (1996)
5. Chekuri, C., Khanna, S., Shepherd, B.: The all-or-nothing multicommodity flow problem. In: Proc. 36th ACM Symposium on Theory of Computing (STOC), pp. 156-165 (2004)
6. Chekuri, C., Khanna, S., Shepherd, B.: Multicommodity flow, well-linked terminals, and routing problems. In: Proc. 37th ACM Symposium on Theory of Computing (STOC), pp. 183-192 (2005)
7. Chekuri, C., Khanna, S., Shepherd, B.: An O(√n) approximation and integrality gap for disjoint paths and unsplittable flow. Theory of Computing 2, 137-146 (2006)
8. Even, S., Itai, A., Shamir, A.: On the complexity of timetable and multicommodity flow problems. SIAM Journal on Computing 5, 691-703 (1976)
9. Frank, A.: Packing paths, cuts and circuits - a survey. In: Korte, B., Lovász, L., Promel, H.J., Schrijver, A. (eds.) Paths, Flows and VLSI-Layout, pp. 49-100. Springer, Berlin (1990)
10. Guruswami, V., Khanna, S., Rajaraman, R., Shepherd, B., Yannakakis, M.: Nearoptimal hardness results and approximaiton algorithms for edge-disjoint paths and related problems. J. Comp. Syst. Science 67, 473-496 (2003);
11. Also Proc. 31st ACM Symposium on Theory of Computing (STOC), pp. 19-28 (1999)
12. Jung, H.A.: Verallgemeinerung des n-Fachen Zusammenhangs fuer Graphen. Math. Ann. 187, 95-103 (1970)
13. Kawarabayashi, K., Reed, B.: A nearly linear time algorithm for the half integral disjoint paths packing. In: Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 446-454 (2008)
14. Kawarabayashi, K., Kobayashi, Y.: Improved algorithm for the half-disjoint paths problem. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds.) APPROX 2010, LNCS, vol. 6302, pp. 287-297. Springer, Heidelberg (2010)
15. Kawarabayashi, K., Kobayashi, Y.: An O(log n)-approximation algorithm for the disjoint paths problem in Eulerian planar graphs and 4-edge-connected planar graphs. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds.) APPROX 2010, LNCS, vol. 6302, pp. 274-286. Springer, Heidelberg (2010)
16. Kawarabayashi, K., Wollan, P.: A shorter proof of the Graph Minor Algorithm - The Unique Linkage Theorem. In: Proceeding of the 42nd ACM Symposium on Theory of Computing (STOC 2010), pp. 687-694 (2010)
17. Kawarabayashi, K., Kobayashi, Y., Reed, B.: The disjoint paths problem in quadratic time (submitted), http://research.nii.ac.jp/~k-keniti/quaddp1.pdf
18. Kawarabayashi, K., Kobayashi, Y.: The edge disjoint paths problem in eulerian graphs and 4-edge-connected graphs. In: Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 345-353 (2010)
19. Kawarabayashi, K., Kobayashi, Y.: Breaking the O(√n)-approximation algorithm for the disjoint paths problem (preprint)
20. Kleinberg, J.: Decision algorithms for unsplittable flow and the half-disjoint paths problem. In: Proc. 30th ACM Symposium on Theory of Computing (STOC), pp. 530-539 (1998)
21. Kleinberg, J.: An approximation algorithm for the disjoint paths problem in evendegree planar graphs. In: Proc. 46th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 627-636 (2005)
22. Kleinberg, J., Tardos, É.: Disjoint paths in densely embedded graphs. In: Proc. 36th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 52-61 (1995)
23. Kleinberg, J., Tardos, É.: Approximations for the disjoint paths problem in high-diameter planar networks. In: Proc. 27th ACM Symposium on Theory of Computing (STOC), pp. 26-35 (1995)
24. Kolliopoulos, S., Stein, C.: Improved approximation algorithms for unsplittable flow problems. In: Proc. 38th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 426-435 (1997)
25. Kramer, M.R., van Leeuwen, J.: The complexity of wire-routing and finding minimum area layouts for arbitrary VLSI circuits. Adv. Comput. Res. 2, 129-146 (1984)
26. Larman, D.G., Mani, P.: On the Existence of Certain Configurations Within Graphs and the 1-Skeletons of Polytopes. Proc. London Math. Soc. 20, 144-160 (1974)
27. Raghavan, P., Thompson, C.D.: Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica 7, 365-374 (1987)
28. Rao, S., Zhou, S.: Edge disjoint paths in moderately connected graphs. SIAM J. Computing 39, 1856-1887 (2010)
29. Reed, B.: Tree width and tangles: a new connectivity measure and some applications. In: Surveys in Combinatorics. London Math. Soc. Lecture Note Ser., vol. 241, pp. 87-162. Cambridge Univ. Press, Cambridge (1997)
30. Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B 63, 65-110 (1995)
31. Robertson, N., Seymour, P.D.: Graph minors. XVI. Excluding a non-planar graph. J. Combin. Theory Ser. B 89, 43-76 (2003)
32. Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Algorithm and Combinatorics, vol. 24. Springer, Heidelberg (2003)
33. Srinviasan, A.: Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems. In: Proc. 38th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 416-425 (1997)
34. Thomas, R., Wollan, P.: An improved linear edge bound for graph linkages. European J. Combin. 26, 309-324 (2005)
35. Thomassen, C.: 2-linked graph. European Journal of Combin. 1, 371-378 (1980)