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arXiv · 1408.5958

On the Path-Width of Integer Linear Programming

Constantin Enea·Peter Habermehl·Omar Inverso·Gennaro Parlato
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Abstract

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of path-width at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded path- width, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification.

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Constantin Enea, Peter Habermehl, Omar Inverso, Gennaro Parlato. 2014-08-26. On the Path-Width of Integer Linear Programming. https://doi.org/10.4204/eptcs.161.9

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