An application of simultaneous diophantine approximation in combinatorial optimization
 András Frank,
 Éva Tardos
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We present a preprocessing algorithm to make certain polynomial time algorithms strongly polynomial time. The running time of some of the known combinatorial optimization algorithms depends on the size of the objective functionw. Our preprocessing algorithm replacesw by an integral valuedw whose size is polynomially bounded in the size of the combinatorial structure and which yields the same set of optimal solutions asw.
As applications we show how existing polynomial time algorithms for finding the maximum weight clique in a perfect graph and for the minimum cost submodular flow problem can be made strongly polynomial.
Further we apply the preprocessing technique to make H. W. Lenstra’s and R. Kannan’s Integer Linear Programming algorithms run in polynomial space. This also reduces the number of arithmetic operations used.
The method relies on simultaneous Diophantine approximation.
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 Title
 An application of simultaneous diophantine approximation in combinatorial optimization
 Journal

Combinatorica
Volume 7, Issue 1 , pp 4965
 Cover Date
 19870301
 DOI
 10.1007/BF02579200
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 68 E 10
 Industry Sectors
 Authors

 András Frank ^{(1)}
 Éva Tardos ^{(2)}
 Author Affiliations

 1. Institute of Mathematics, Eötvös University, P. O. B. 323, 1445, Budapest, Hungary
 2. Institute of Mathematics, Eötvös University, P. O. B. 323, 1445, Budapest, Hungary