{"type":"ScholarlyArticle","title":"Approximating Integer Solution Counting via Space Quantification for Linear Constraints","authors":[{"name":"Cunjing Ge","slug":"cunjing-ge","given":"Cunjing","family":"Ge","affiliation":"State Key Laboratory of Computer Science , ISCAS; University of Chinese Academy of Sciences"},{"name":"Feifei Ma","slug":"feifei-ma","given":"Feifei","family":"Ma","affiliation":"State Key Laboratory of Computer Science , ISCAS; Laboratory of Parallel Software and Computational Science , ISCAS; University of Chinese Academy of Sciences"},{"name":"Xutong Ma","slug":"xutong-ma","given":"Xutong","family":"Ma","affiliation":"State Key Laboratory of Computer Science , ISCAS; University of Chinese Academy of Sciences"},{"name":"Fan Zhang","slug":"fan-zhang","given":"Fan","family":"Zhang","affiliation":"State Key Laboratory of Computer Science , ISCAS; University of Chinese Academy of Sciences"},{"name":"Pei Huang","slug":"pei-huang","given":"Pei","family":"Huang","affiliation":"State Key Laboratory of Computer Science , ISCAS; University of Chinese Academy of Sciences"},{"name":"Jian Zhang","slug":"jian-zhang","given":"Jian","family":"Zhang","affiliation":"State Key Laboratory of Computer Science , ISCAS; University of Chinese Academy of Sciences"}],"abstract":"Solution counting or solution space quantification (means volume computation and volume estimation) for linear constraints (LCs) has found interesting applications in various fields. Experimental data shows that integer solution counting is usually more expensive than quantifying volume of solution space while their output values are close. So it is helpful to approximate the number of integer solutions by the volume if the error is acceptable. In this paper, we present and prove a bound of such error for LCs. It is the first bound that can be used to approximate the integer solution counts. Based on this result, an approximate integer solution counting method for LCs is proposed. Experiments show that our approach is over 20x faster than the state-of-the-art integer solution counters. Moreover, such advantage increases with the problem scale.","doi":"10.24963/ijcai.2019/235","url":"https://ijcai.org/proceedings/2019/235","pdf":"https://ijcai.org/proceedings/2019/0235.pdf","markdown":"https://ijcai.org/proceedings/2019/235.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/235","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":235,"pages":{"first":1697,"last":1703},"keywords":["Constraints and SAT: Other approaches","Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving"],"videos":[],"references":[{"position":1,"raw":"[Abío and Stuckey, 2014] Ignasi Abío and Peter J. 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