Minimum 0-extensions of graph metrics

European Journal of Combinatorics

Volumn 19, Issue 1, 1998, Pages 71-101

  Karzanov, Alexander V ^a  

^a INSTITUTE FOR SYSTEMS ANALYSIS   (Russian Federation)

Author keywords

Finite metric; Isometric embedding; Metric extension; Multi(commodity) flow; Multiterminal cut

Indexed keywords

EID: 0041940683     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1006/eujc.1997.0154     Document Type: Article

References (19)

1. D. Avis, On the extreme rays of the metric cone, Can. J. Math., 32 (1980), 126-144.
2. H.-J. Bandelt, Hereditary modular graphs, Combinatorica, 8(2) (1988), 149-157.
3. B. V. Cherkassky, A solution of a problem on multicommodity flows in a network, Ekonomika i Matematicheskie Metody, 13(1) (1977), 143-151, in Russian.
4. E. Dalhaus, D. S. Johnson, C. Papadimitriou, P. Seymour, and M. Yannakakis, The complexity of the multiterminal cuts, SIAM J. Comput. 23(4) (1994) 864-894.
5. A. W. M. Dress, Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups, Adv. Math., 53 (1984), 321-402.
6. L. R. Ford and D. R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
7. M. Grötshel, L. Lovász, and A. Shrijver, Geometric Algorithms and Combinatorial Optimization, Springer, Berlin, 1988.
8. J. Isbell, Six theorems about metric spaces, Comment. Math. Helv., 39 (1964), 65-74.
9. A. V. Karzanov, A generalized MFMC-property and multicommodity cut problems, in: Finite and Infinite Sets (Proc. 6th Hungar. Comb. Coll., Eger, 1981), North-Holland, Amsterdam, 1984, Vol. 2, pp. 443-486.
10. A. V. Karzanov, Half-integral five-terminus flows, Disc. Appl. Math., 18(3) (1987), 263-278.
11. A. V. Karzanov, Polyhedra related to undirected multicommodity flows, Lin. Alg. Applic., 114-115 (1989), 293-328.
12. A. V. Karzanov, Minimum distance mappings of graphs, Tech. Report 982, LRI, Université Paris-XI, 1995, 33pp.
13. A. V. Karzanov and M. V. Lomonosov, Systems of flows in undirected networks, in: Mathematical Programming etc., Institute for System Studies, Moscow, 1978, issue 1, pp. 59-66, in Russian.
14. A. V. Karzanov and Y. Manoussakis, Minimum (2, r)-metrics and integer multiflows, Europ. J. Combinatorics, 17 (1996), 223-232.
15. M. V. Lomonosov, On a system of flows in a network, Problemy Peredatchi Informacii, 14 (1978), 60-73, in Russian.
16. M. V. Lomonosov, Combinatorial approaches to multiflow problems, Disc. Appl. Math., 11(1) (1985), 1-94.
17. L. Lovász, On some connectivity properties of Eulerian graphs, Acta Math. Acad. Sci. Hungaricae, 28 (1976), 129-138.
18. V. A. Rokhlin and D. B. Fuks, Introduction in Topology, Nauka, Moscow, 1977, in Russian.
19. E. Tardos, A strongly polynomial algorithm to solve combinatorial linear programs, Oper. Res., 34 (1986), 250-256.