The clustering matroid and the optimal clustering tree

Mathematical Programming

Volumn 98, Issue 1-3, 2003, Pages 385-414

  Korach, Ephraim ^a   Stern, Michal ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Clustering spanning trees; Combinatorial optimization; Hypergraphs; Matroids; Polyhedra; Polynomial graph algorithms; Primal dual algorithms

Indexed keywords

HYPER GRAPH; POLYHEDRA; POLYNOMIAL GRAPH; PRIMAL DUAL ALGORITHMS; SPANNING TREE;

COMBINATORIAL MATHEMATICS; COMBINATORIAL OPTIMIZATION; COSTS; FAULT TOLERANCE; GEOMETRY; MATRIX ALGEBRA; TREES (MATHEMATICS);

CLUSTERING ALGORITHMS;

EID: 33744934992     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-003-0410-x     Document Type: Conference Paper

References (15)

1. Bixby, R.E.: Recent Algorithms for Two Versions of Graph Realization and Remarks onApplications to Linear Programming, Progress in Combinatorial Optimization, W.R. Pulleyblank (Ed.), Academic Press Canada 1984, pp. 39-67
2. Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications, American Elsevier Publishing, NewYork, 1976
3. Booth, K.S., Leuker, G.S.:Testing for the Consecutive Ones Property, Interval Graph and Graph Planarity Using PQ-Tree Algorithms. J. Comp. Sys. Sci. 13, 335-379 (1976)
4. Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. John Wiley and Sons, New York, 1998
5. Edmonds, J.: Matroids, Submodular Functions, and Certain Polyhedra in Combinatorial Structures and their Applications (R.K. Guy, H. Hanani, N. Sauer, J. Schonheim, eds.), Gordon and Breach, NewYork, 1970 pp. 69-87
6. Edmonds, J.: Matroids and the Greedy Algorithm. Mathematical Programming 1, 127-136 (1971)
7. Garey, M.R., Johnson, D.S.: Computers and Intractability, A guide to the theory of NP-Completeness. W.H. Freeman and Company, San Francisco, 1979
8. Gavril, F.:A Recognition Algorithm for the Intersection Graphs of Paths in Trees. Discrete Mathematics 23, 211-227 (1978)
9. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980
10. Golumbic, M.C., Jamison, R.E.: Edge and Vertex Intersection of Paths in a Tree. Discrete Mathematics, North-Holland 55, 151-159 (1985)
11. Korach, E., Stern, M.: The Clustering TSP Problem. In preparation
12. McKee, T.A., McMorris, F.R.: Topics in Intersection Graph Theory. SIAM Monographs on Discrete Mathematics and Applications, 1999
13. Rado, R.: A Note on Independence Functions. Proceedings of the London Mathematical Society 7, 300-320 (1957)
14. Swaminathan, R., Wagner, D.K.: On the Consecutive-Retrieval Problem. SIAM J. Comp. 23(2), 398-414 (1994)
15. Welsh, D.J.A.: Matroid Theory. Academic Press, London, 1976