Edge-connectivity augmentation with partition constraints

SIAM Journal on Discrete Mathematics

Volumn 12, Issue 2, 1999, Pages 160-207

  Bang Jensen, Jørgen ^a   Gabow, Harold N ^b   Jordán, Tibor ^a   Szigeti, Zoltán ^c  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^b University of Colorado at Boulder   (United States)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; POLYNOMIALS; PROBLEM SOLVING; SET THEORY;

BIPARTITE GRAPHS; COMBINATORIAL ALGORITHMS; EDGE-CONNECTIVITY AUGMENTATION PROBLEMS; UNDIRECTED GRAPHS;

GRAPH THEORY;

EID: 0032624453     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480197324700     Document Type: Article

References (22)

1. J. BANG-JENSEN AND T. JORDÁN, Edge-connectivity augmentation preserving simplicity, SIAM J. Disc. Math., 11 (1998), pp. 603-623.
2. E.D. BOLKER AND H. CRAPO, How to brace a one-story building, Environ. Plan. B, 4 (1977), pp. 125-152.
3. G.-R. CAI AND Y.-G. SUN, The minimum augmentation of any graph to a k-edge-connected graph, Networks, 19 (1989), pp. 151-172.
4. E. CHENG AND T. JORDÁN, Successive edge-connectivity augmentation problems, Math. Programming, Ser. B., to appear.
5. K.P. ESWARAN AND R.E. TARJAN, Augmentation problems, SIAM J. Comput., 5 (1976), pp. 653-665.
6. A. FRANK, Augmenting graphs to meet edge-connectivity requirements, SIAM J. Disc. Math., 5 (1992), pp. 25-53.
7. A. FRANK, Connectivity augmentation problems in network design, Math. Programming: State of the Art 1994, J.R. Birge and K.G. Murty, eds., University of Michigan, Ann Arbor, MI, 1994, pp. 34-63.
8. H.N. GABOW AND T. JORDÁN, How to make a square grid framework with cables rigid, Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, 1999, pp. 356-365.
9. M. GRÖTSCHEL, C.L. MONMA, AND M. STOER, Design of survivable networks, Handbooks in Oper. Res. Management Sci. 7, Network Models, M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser, eds., North-Holland, Amsterdam, 1994, pp. 617-672.
10. S. L. HAKIMI, On realizability of a set of integers as degrees of the vertices of a linear graph, J. SIAM, 10 (1962), pp. 496-506.
11. T.-S. HSU AND M.-Y. KAO, Optimal augmentation for bipartite componentwise biconnectivity in linear time, Algorithms Comput., Lecture Notes in Comput. Sci. 1178, Springer-Verlag, Berlin, 1996.
12. T. JORDÁN, Two NP-Complete Augmentation Problems, Preprint 8, Department of Math and Computer Science, Odense University, Odense, Denmark, 1997.
13. G. KANT AND H.L. BODLAENDER, Planar graph augmentation problems, Algorithms and Data Structures, Lecture Notes in Comput. Sci. 519, Springer-Verlag, Berlin, 1991.
14. L. LOVÁSZ, Combinatorial Problems and Exercises, North-Holland, Amsterdam, 1979.
15. W. MADER, A reduction method for edge-connectivity in graphs, Ann. Discrete Math., 3 (1978), pp. 145-164.
16. H. NAGAMOCHI AND T. IBARAKI, Computing edge-connectivity of multigraphs and capacitated graphs, SIAM J. Discrete Math., 5 (1992), pp. 54-66.
17. H. NAGAMOCHI AND T. IBARAKI, Deterministic Õ(nm) time edge-splitting algorithm in undirected graphs, J. Combin. Optim., 1 (1997), pp. 5-46.
18. H. NAGAMOCHI, S. NAKAMURA, AND T. IBARAKI, A simple Õ(nm) time edge-splitting algorithm in undirected graphs, Tech. report 96013, Department of Applied Mathematics and Physics, Kyoto University, Kyoto, Japan, 1996.
19. D. NAOR, D. GUSFIELD, AND CH. MARTEL, A fast algorithm for optimally increasing the edge connectivity, SIAM J. Comput., 26 (1997), pp. 1139-1165.
20. A. RECSKI, Matroid Theory and its Applications in Electric Network Theory and in Statics, Akadémiai Kiadó, Budapest, 1989.
21. M. STOER, Design of Survivable Networks, Ph.D. thesis, Lecture Notes in Math. 1531, Springer-Verlag, Berlin, 1992.
22. T. WATANABE AND A. NAKAMURA, Edge-connectivity augmentation problems, J. Comput. System Sci., 35 (1987), pp. 96-144.