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.
74-87
Enea, Constantin
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Habermehl, Peter
bb20bd93-c13d-4fff-b5ce-0d0dc5b7f9e9
Inverso, Omar
1a7b5398-791c-479b-88c9-2442212d0a28
Parlato, Gennaro
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26 August 2014
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
(2014)
On the Path-Width of Integer Linear Programming.
Peron, Adriano and Piazza, Carla
(eds.)
In Proceedings Fifth International Symposium on Games, Automata, Logics and Formal Verification.
vol. 161,
.
(doi:10.4204/EPTCS.161.9).
Record type:
Conference or Workshop Item
(Paper)
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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ILP-GANDALF14.pdf
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Accepted/In Press date: 2014
e-pub ahead of print date: 26 August 2014
Published date: 26 August 2014
Venue - Dates:
Fifth International Symposium on Games, Automata, Logics and Formal Verification (GandALF), Verona, Italy, 2014-09-01
Organisations:
Electronic & Software Systems
Identifiers
Local EPrints ID: 351912
URI: http://eprints.soton.ac.uk/id/eprint/351912
ISSN: 2075-2180
PURE UUID: 26dde00f-b87a-40ef-a14d-b61ba49d9003
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Date deposited: 25 Apr 2013 19:55
Last modified: 16 Mar 2024 03:09
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Contributors
Author:
Constantin Enea
Author:
Peter Habermehl
Author:
Omar Inverso
Author:
Gennaro Parlato
Editor:
Adriano Peron
Editor:
Carla Piazza
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