Phase transitions in integer linear problems

S. Colabrese; D. De Martino; L. Leuzzi; E. Marinari

doi:10.1088/1742-5468/aa85c3

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arXiv · 1705.06303

Phase transitions in integer linear problems

S. Colabrese·D. De Martino·L. Leuzzi·E. Marinari

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Abstract

The resolution of 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 $\alpha=N/M$ 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 ($c$, $\alpha$). We give numerical evidence that the associated computational problems become more difficult across the critical point and in particular in the coexistence region.

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cond-mat.stat-mech cond-mat.dis-nn cs.CC

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S. Colabrese, D. De Martino, L. Leuzzi, E. Marinari. 2017-05-17. Phase transitions in integer linear problems. https://doi.org/10.1088/1742-5468/aa85c3

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