The University of Southampton
University of Southampton Institutional Repository

On the Path-Width of Integer Linear Programming

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.
2075-2180
74-87
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
Peron, Adriano
Piazza, Carla
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
Peron, Adriano
Piazza, Carla

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, pp. 74-87 . (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.

Text
ILP-GANDALF14.pdf - Version of Record
Available under License Creative Commons Attribution.
Download (231kB)

More information

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), Italy, 2014-09-01
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 351912
URI: https://eprints.soton.ac.uk/id/eprint/351912
ISSN: 2075-2180
PURE UUID: 26dde00f-b87a-40ef-a14d-b61ba49d9003

Catalogue record

Date deposited: 25 Apr 2013 19:55
Last modified: 26 Aug 2019 16:30

Export record

Altmetrics

Contributors

Author: Constantin Enea
Author: Peter Habermehl
Author: Omar Inverso
Author: Gennaro Parlato
Editor: Adriano Peron
Editor: Carla Piazza

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×