On the path-width of integer linear programming
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, 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.
257-271
Enea, Constantin
ff289fa8-2db4-45da-95e2-98800897844b
Habermehl, Peter
bb20bd93-c13d-4fff-b5ce-0d0dc5b7f9e9
Inverso, Omar
1a7b5398-791c-479b-88c9-2442212d0a28
Parlato, Gennaro
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1 April 2017
Enea, Constantin
ff289fa8-2db4-45da-95e2-98800897844b
Habermehl, Peter
bb20bd93-c13d-4fff-b5ce-0d0dc5b7f9e9
Inverso, Omar
1a7b5398-791c-479b-88c9-2442212d0a28
Parlato, Gennaro
c28428a0-d3f3-4551-a4b5-b79e410f4923
Enea, Constantin, Habermehl, Peter, Inverso, Omar and Parlato, Gennaro
(2017)
On the path-width of integer linear programming.
Information and Computation, .
(doi:10.1016/j.ic.2016.07.010).
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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Accepted/In Press date: 2 June 2016
e-pub ahead of print date: 29 July 2016
Published date: 1 April 2017
Organisations:
Electronic & Software Systems
Identifiers
Local EPrints ID: 386737
URI: http://eprints.soton.ac.uk/id/eprint/386737
ISSN: 0890-5401
PURE UUID: 174e927a-04a5-4f07-b2a4-a4842c4c41d1
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Date deposited: 30 Jan 2016 22:58
Last modified: 15 Mar 2024 05:23
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Contributors
Author:
Constantin Enea
Author:
Peter Habermehl
Author:
Omar Inverso
Author:
Gennaro Parlato
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