The Phase Transition of the Linear Inequalities Problem

  • Alessandro Armando
  • Felice Peccia
  • Silvio Ranise
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)


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 by adopting a methodology which has been proved very successful on NP-complete problems. The methodology is 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 very large instances by exploiting the technique of finite size scaling.


Phase Transition Constraint Satisfaction Problem Simplex Algorithm Size Scaling Finite Size Scaling 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alessandro Armando
    • 1
  • Felice Peccia
    • 1
  • Silvio Ranise
    • 1
    • 2
  1. 1.DIST-Università degli Studi di GenovaGenovaItaly
  2. 2.LORIA-INRIA-LorraineVillers les NancyCedexFrance

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