Truncated Markov bases and Gröbner bases for Integer Programming

Details Truncated Markov bases and Gröbner bases for Integer Programming Truncated Markov bases and Gröbner bases for Integer Programming

2006-12-20

arxiv.org/abs/math/0612615v1

Mathematics

Optimization and Control

27 pages

Scientific paper

We present a new algorithm for computing a truncated Markov basis of a lattice. In general, this new algorithm is faster than existing methods. We then extend this new algorithm so that it solves the linear integer feasibility problem with promising results for equality knapsack problems. We also present a novel Groebner basis approach to solve a particular integer linear program as opposed to previous Groebner basis methods that effectively solved many different integer linear programs simultaneously. Initial results indicate that this optimisation algorithm performs better than previous Groebner basis methods.

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