Approximate Counting CSP Solutions Using Partition Function
This addresses a computational challenge in AI and optimization, but it appears incremental as it builds on existing techniques like belief propagation.
The paper tackles the problem of counting solutions for constraint satisfaction problems (CSP) by proposing an approximate method based on partition functions and belief propagation, achieving efficient performance on both random and structural problems.
We propose a new approximate method for counting the number of the solutions for constraint satisfaction problem (CSP). The method derives from the partition function based on introducing the free energy and capturing the relationship of probabilities of variables and constraints, which requires the marginal probabilities. It firstly obtains the marginal probabilities using the belief propagation, and then computes the number of solutions according to the partition function. This allows us to directly plug the marginal probabilities into the partition function and efficiently count the number of solutions for CSP. The experimental results show that our method can solve both random problems and structural problems efficiently.