On the Path-Width of Integer Linear Programming
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, w...
| Published in: | Electronic Proceedings in Theoretical Computer Science |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2014-08-01
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| Online Access: | http://arxiv.org/pdf/1408.5958v1 |
| Summary: | 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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| ISSN: | 2075-2180 |