Efficient splitting off algorithms for graphs

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129502, Issue , 1994, Pages 696-705

  Gabow, Harold N ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; FLOW GRAPHS; GRAPHIC METHODS; POLYNOMIAL APPROXIMATION; GRAPH THEORY; MATHEMATICAL MODELS; POLYNOMIALS; THEOREM PROVING;

CONNECTIVITY PROBLEMS; EDGE CONNECTIVITY; EDGE CONNECTIVITY AUGMENTATION PROBLEMS; EFFICIENT COMPUTATION; GRAPH TRANSFORMATION; LOCAL CONNECTIVITY; POLYNOMIAL-TIME ALGORITHMS; WELL-BALANCED ORIENTATION;

DIRECTED GRAPHS; ALGORITHMS;

EDGE CONNECTIVITY AUGMENTATION PROBLEM; MADER'S THEOREM; SPLITTING; UNDIRECTED AND DIRECTED MULTIGRAPHS;

EID: 0028123965     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/195058.195436     Document Type: Conference Paper

References (20)

1. [B] A.A. Benczur, "Augmenting undirected connectivity in o(n3) time", these proceedings.
2. [E69] J. Edmonds, "Submodular functions, matroids, and certain polyhedra", Calgary International Conf. on Combinatorial Structures and their Applications, Gordon and Breach, New York, 1969, pp. 69-87.
3. [F82] A. Frank, "An algorithm for submodular functions on graphs", in Bonn Workshop on Combinatorial Optimization, A. Bachem, M. Grotschel and B. Korte, Eds., Ann. Discrete Math., 16, North- Holland, Amsterdam, 1982, pp. 97-120.
4. [F84] A. Frank, "Finding feasible vectors of Edmonds- Giles polyhedra", J. Comb. Th., B, SB, 1984, pp. 221-239.
5. [F92a] A. Frank, "Augmenting graphs to meet edge- connectivity requirements'', SIAM J. Disc. Math., 5, 1, 1992, pp. 25-53.
6. [F92b] A. Frank, "On a theorem of Mader", Discrete Mathematics 101, 1992, pp. 49-57.
7. [F93] A.Frank, "Applications of submodular functions", in Surveys in Combinatorics, London Math. Soc. Lecture Notes Series 187, K. Walker, Ed., Cam-bridge Univ. Press, NY, 1993, pp. 85-136.
8. [FF] L.R. Ford Jr. and D.R. Fulkerson, Flows in Networks, Princeton Univ. Press, Princeton, NJ, 1962.
9. [Ga91a] H.N. Gabow, "A matroid approach to finding edge connectivity and packing arborescences", Proc. 23rd Annual ACM Symp. on Theory of Comp., pp. 112-122; J. CSS, to appear.
10. [Ga91b] H.N. Gabow, "Applications of a poset representation to edge connectivity and graph rigidity", Proc. 32nd Annual Symp. on Found, of Comp. Sci., 1991, pp. 812-821; also Tech. Rept. CU-CS- 545-91, Dept. of Comp. Sci., Univ. of Col. at Boulder, Boulder, CO, 1991.
11. [Ga93a] H.N. Gabow, "A representation for crossing set families with applications to submodular flow problems", Proc. 4th Annual ACM-SIAM Symp. on Disc. Algorithms, 1993, pp. 202-211; "Centroids, representations and submodular flows", submitted for publication.
12. [Ga93b] H.N. Gabow, "A framework for cost-scaling algorithms for submodular flow problems", Proc. 34th Annual Symp. on Found, of Comp. Sci., 1993, pp. 449-458; also Tech. Rept. CU-CS-661-93, Dept. of Comp. Sci., Univ. of Col. at Boulder, Boulder, CO, 1993.
13. [HO] J. Hao and J.B. Orlin, "A faster algorithm for finding the minimum cut in a graph", Proc. 3rd Annual ACM-SIAM Symp. on Disc. Algorithms, pp. 165-174.
14. [L] L. Lovasz, Combinatorial Problems and Exercises, 2nd Ed., North-Holland, New York, 1993.
15. [M] W. Mader, "A reduction method for edge- connectivity in graphs", Ann. Discrete Math., 3, 1978, pp. 145-164.
16. [NGM] D. Naor, D. Gusfield and C. Martel, "A fast algorithm for optimally increasing the edge- connectivity", Proc. 31st Annual Symp. on Found, of Comp. Sci., 1990, pp. 698-707.
17. [NI] H. Nagamochi and T. Ibaraki, "A linear-Time algorithm for finding a sparse lb-connected spanning subgraph of a ?-connected graph", Algorithmica, 7, 1992, pp. 583-596.
18. [NW] C. J. A. Nash-Williams, "On orientations, connectivity and odd vertex pairings in finite graphs", Canadian J. Math., 12, 1960, pp. 555-567.
19. H. E. Robbins, "A theorem on graphs with an ap plication to a problem of traffic control", American Math. Monthly, 46, 1939, pp. 281-283.
20. [TTT] Tardos, C.A. Tovey and M.A. Trick, "Layered augmenting path algorithms", Math. Op. Res., 11, 2, 1986, pp. 362-370.