Colourful linear programming and its relatives

Mathematics of Operations Research

Volumn 22, Issue 3, 1997, Pages 550-567

  Bárány, Imre ^a   Onn, Shmuel ^b  

^a ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

P; Carath odory's theorem; Combinatorial geometry; Computational complexity; Enumeration; Integer programming; Linear programming; Matroid; NP; Partition; Permanent; Polytope; Transversal; Tverberg's theorem

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; DECISION THEORY; INTEGER PROGRAMMING; ITERATIVE METHODS; LINEAR ALGEBRA; PROBLEM SOLVING; SET THEORY;

CARATHEODORY THEOREM; MATROID BASIS NONBASIS PROBLEMS; TVERBERG'S THEOREM;

LINEAR PROGRAMMING;

EID: 0031207981     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.22.3.550     Document Type: Article

References (15)

1. Alon, N., I. Bárány, Z. Füredi, D. Kleitman (1992). Point selections and weake-nets for convex hulls. Combin. Prob. Comp. 1 189-200.
2. _, D. Kleitman (1992). Piercing convex sets and the Hadwiger-Debrunner (p, q)-problem. Adv. Math. 96 103-112.
3. Bárány, I. (1982). A generalization of Carathéodory's theorem. Discr. Math. 40 141-152.
4. Blum, L., M. Snub, S. Smale (1989). On a theory of computation and complexity over the real numbers. Bull. AMS 21 1-46.
5. Chazelle, B., H. Edelsbrunner, M. Grigni, L. Guibas, M. Sharir, E. Welzl (1995). Weak ε-nets for convex sets. Discr. Comp. Geom. 13 1-17.
6. -2 iterations, Report SOL/92/5, Systems Optimization Laboratory, Department of Operations Research, Stanford University.
7. Freund, R. (1995). Personal communication.
8. Garey, M. R., D. S. Johnson (1979). Computers and Intractability, W. H. Freeman, San Francisco.
9. Kleinschmidt, P., S. Onn (1996). Signable posets and partitionable simplicial complexes. Discr. Comp. Geom. 15 443-466.
10. Onn, S. (1991). On the geometry and computational complexity of Radon partitions in the integer lattice. SIAM J. Discr. Math. 4 436-447.
11. _ (1997). A colorful determinantal identity, a conjecture of Rota, and Latin squares. Amer. Math. Monthly 104 156-159.
12. Sarkaria, K. S. (1992). Tverberg's theorem via number fields. Israel J. Math. 79 317-320.
13. Schrijver, A. (1986). Theory of Linear and Integer Programming, John Wiley, New York.
14. Tverberg, H. (1966). A generalization of Radon's theorem J. London Math. Soc. 41 123-128.
15. Valiant, L. G. (1979). The complexity of computing the permanent. Theor. Comput. Scr. 8 189-201.