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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 111
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING
Edited by:
Paper 29

Discrete Optimization and Initial Value Problem for System of Ordinary Differential Equations

S. Szabó and B. Zaválnij

Faculty of Sciences, University of Pécs, Hungary

Full Bibliographic Reference for this paper
, "Discrete Optimization and Initial Value Problem for System of Ordinary Differential Equations", in , (Editors), "Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 29, 2017. doi:10.4203/ccp.111.29
Keywords: combinatorial optimization, maximum cliques, zero-one linear programming, greedy coloring, matrix game, differential equations, practical solutions of NP complete problems .

Summary
In 1950 G. W. Brown and J. von Neumann reduced the solution of a linear program to an initial value problem of a system of ordinary differential equations. The paper presents an algorithm to modify the constraints of the edge based zero-one linear programming equivalent of the maximum clique problem. The method of differential equations was applied to collect numerical evidence that the real relaxation of the modified form may sharpen the upper bound for the clique size.

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