Phase transitions in integer linear problems

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OA https://arxiv.org/abs/1705.06303 [Submitted Version]

Journal Article | Published | English

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Author
Colabrese, Simona; De Martino, DanieleISTA ; Leuzzi, Luca; Marinari, Enzo
Department
Abstract
The resolution of a linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density c and the ratio α=N/M between number of variables N and number of constraints M. By means of ensemble calculations we show that the space of feasible solutions endows a Van-Der-Waals phase diagram in the plane (c, α). We give numerical evidence that the associated computational problems become more difficult across the critical point and in particular in the coexistence region.
Publishing Year
Date Published
2017-09-26
Journal Title
Journal of Statistical Mechanics: Theory and Experiment
Publisher
IOP Publishing
Volume
2017
Issue
9
Article Number
093404
ISSN
IST-REx-ID
823
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