The ellipsoid method and its consequences in combinatorial optimization
 M. Grötschel,
 L. Lovász,
 A. Schrijver
 … show all 3 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
L. G. Khachiyan recently published a polynomial algorithm to check feasibility of a system of linear inequalities. The method is an adaptation of an algorithm proposed by Shor for nonlinear optimization problems. In this paper we show that the method also yields interesting results in combinatorial optimization. Thus it yields polynomial algorithms for vertex packing in perfect graphs; for the matching and matroid intersection problems; for optimum covering of directed cuts of a digraph; for the minimum value of a submodular set function; and for other important combinatorial problems. On the negative side, it yields a proof that weighted fractional chromatic number is NPhard.
 Title
 The ellipsoid method and its consequences in combinatorial optimization
 Journal

Combinatorica
Volume 1, Issue 2 , pp 169197
 Cover Date
 198106
 DOI
 10.1007/BF02579273
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 90 C XX, 05 C XX
 90 C 25, 90 C 10
 Industry Sectors
 Authors

 M. Grötschel ^{(1)}
 L. Lovász ^{(2)}
 A. Schrijver ^{(3)}
 Author Affiliations

 1. Universität Bonn, Inst. für Ökonometrie und Operations Research, D5300, Bonn, F.R.G.
 2. Bolyai Institute, A. József University, H6720, Szeged, Hungary
 3. Inst. Actuariaat en Econometrie, University of Amsterdam, Amsterdam, The Netherlands