Random generation of combinatorial structures from a uniform
Theoretical Computer Science
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Machine Learning
Adaptive simulated annealing: A near-optimal connection between sampling and counting
Journal of the ACM (JACM)
Approximate counting by sampling the backtrack-free search space
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
From sampling to model counting
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Computing the density of states of Boolean formulas
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
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Consider a combinatorial state space S, such as the set of all truth assignments to N Boolean variables. Given a partition of S, we consider the problem of estimating the size of all the subsets in which S is divided. This problem, also known as computing the density of states, is quite general and has many applications. For instance, if we consider a Boolean formula in CNF and we partition according to the number of violated constraints, computing the density of states is a generalization of both SAT, MAXSAT and model counting. We propose a novel Markov Chain Monte Carlo algorithm to compute the density of states of Boolean formulas that is based on a flat histogram approach. Our method represents a new approach to a variety of inference, learning, and counting problems. We demonstrate its practical effectiveness by showing that the method converges quickly to an accurate solution on a range of synthetic and real-world instances.