On the path-width of integer linear programming

Enea, Constantin, Habermehl, Peter, Inverso, Omar and Parlato, Gennaro (2017) On the path-width of integer linear programming Information and Computation, pp. 257-271. (doi:10.1016/j.ic.2016.07.010).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.ic.2016.07.010
ISSNs: 0890-5401 (print)
Organisations: Electronic & Software Systems
ePrint ID: 386737
Date :
Date Event
2 June 2016Accepted/In Press
29 July 2016e-pub ahead of print
1 April 2017Published
Date Deposited: 30 Jan 2016 22:58
Last Modified: 17 Jun 2017 16:32
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/386737

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