Threshold behaviors of a random constraint satisfaction problem with exact phase transitions

Authors:
Chunyan Zhao;Zhiming Zheng
Affiliations:
School of Mathematics and Systems Science, Beihang University, Beijing 100191, China and Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, China;School of Mathematics and Systems Science, Beihang University, Beijing 100191, China and Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, China
Venue:
Information Processing Letters
Year:
2011

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Abstract

We consider a random constraint satisfaction problem named model RB, which exhibits a sharp satisfiability phase-transition phenomenon when the control parameters pass through the critical values denoted by r"c"r and p"c"r. Using finite-size scaling analysis, we bound the width of the transition region for finite problem size n, which might be the first rigorous study on the threshold behaviors of NP-complete problems.