The Phase Transition of the Linear Inequalities Problem

Authors:
Alessandro Armando;Felice Peccia;Silvio Ranise
Affiliations:
-;-;-
Venue:
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Year:
2001

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Abstract

One of the most important problems in the polynomial class is checking the satisfiabilityof systems of linear inequalities over the rationals. In this paper, we investigate the phase-transition behavior of this problem byadopting a methodologywhic h has been proved verysuccessful on NP-complete problems. The methodologyis based on the concept of constrainedness, which characterizes an ensemble of randomly generated problems and allows to predict the location of the phase transition in solving such problems. Our work complements and confirms previous results obtained for other polynomial problems. The approach provides a new characterization of the performance of the Phase I of the Simplex algorithm and allows us to predict its behavior on verylarge instances byexploiting the technique of finite size scaling.