{"type":"ScholarlyArticle","title":"A Flat Histogram Method for Computing the Density of States of Combinatorial Problems","authors":[{"name":"Stefano Ermon","slug":"stefano-ermon","given":"Stefano","family":"Ermon","affiliation":""},{"name":"Carla P. Gomes","slug":"carla-p-gomes","given":"Carla P.","family":"Gomes","affiliation":""},{"name":"Bart Selman","slug":"bart-selman","given":"Bart","family":"Selman","affiliation":""}],"abstract":"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.","doi":"10.5591/978-1-57735-516-8/IJCAI11-434","url":"https://ijcai.org/proceedings/2011/434","pdf":"https://ijcai.org/proceedings/2011/0434.pdf","markdown":"https://ijcai.org/proceedings/2011/434.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/434","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":434,"pages":{"first":2608,"last":2612},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}