Counting Solutions of Constraint Satisfiability Problems:Exact Phase Transitions and Approximate Algorithm

02/24/2011
by   Minghao Yin, et al.
0

The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of Constraint Satisfaction Problems (#CSP). We consider the random model, i.e. RB model. We prove that phase transition of #CSP does exist as the number of variables approaches infinity and the critical values where phase transitions occur are precisely located. Preliminary experimental results also show that the critical point coincides with the theoretical derivation. Moreover, we propose an approximate algorithm to estimate the expectation value of the solutions number of a given CSP instance of RB model.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/16/2000

Exact Phase Transitions in Random Constraint Satisfaction Problems

In this paper we propose a new type of random CSP model, called Model RB...
research
02/09/2017

Phase Transitions of the Typical Algorithmic Complexity of the Random Satisfiability Problem Studied with Linear Programming

The Boolean Satisfiability problem asks if a Boolean formula is satisfia...
research
09/23/2022

The cavity method: from exact solutions to algorithms

The goal of this chapter is to review the main ideas that underlie the c...
research
04/30/2014

Phase transitions in semisupervised clustering of sparse networks

Predicting labels of nodes in a network, such as community memberships o...
research
11/05/2020

Exact Phase Transitions of Model RB with Slower-Growing Domains

The second moment method has always been an effective tool to lower boun...
research
02/26/2018

The replica symmetric phase of random constraint satisfaction problems

Random constraint satisfaction problems play an important role in comput...
research
03/09/2021

Smoothed counting of 0-1 points in polyhedra

Given a system of linear equations ℓ_i(x)=β_i in an n-vector x of 0-1 va...

Please sign up or login with your details

Forgot password? Click here to reset