{"type":"ScholarlyArticle","title":"Engineering an Efficient Approximate DNF-Counter","authors":[{"name":"Mate Soos","slug":"mate-soos","given":"Mate","family":"Soos","affiliation":""},{"name":"Divesh Aggarwal","slug":"divesh-aggarwal","given":"Divesh","family":"Aggarwal","affiliation":"National University of Singapore , Singapore; The Centre for Quantum Technologies (CQT) , Singapore"},{"name":"Sourav Chakraborty","slug":"sourav-chakraborty","given":"Sourav","family":"Chakraborty","affiliation":"Indian Statistical Institute , Kolkata"},{"name":"Kuldeep S. Meel","slug":"kuldeep-s-meel","given":"Kuldeep S.","family":"Meel","affiliation":"National University of Singapore , Singapore"},{"name":"Maciej Obremski","slug":"maciej-obremski","given":"Maciej","family":"Obremski","affiliation":"The Centre for Quantum Technologies (CQT) , Singapore"}],"abstract":"Model counting is a fundamental problem with many practical applications, including query evaluation in probabilistic databases and failure-probability estimation of networks. In this work, we focus on a variant of this problem where the underlying \r\n formula is expressed in Disjunctive Normal Form (DNF), also known as #DNF. This problem has been shown to be #P-complete, making it intractable to solve exactly. Much research has therefore been focused on obtaining approximate solutions, particularly in the form of (epsilon, delta) approximations.\r\n\r\nThe primary contribution of this paper is a new approach, called pepin, to approximate #DNF counting that achieves (nearly) optimal time complexity and outperforms \r\nexisting FPRAS. Our approach is based on the recent breakthrough in the context of union of \r\nsets in streaming. We demonstrate the effectiveness of our approach through extensive experiments and show that it provides an affirmative answer to the challenge of efficiently computing #DNF.","doi":"10.24963/ijcai.2023/226","url":"https://ijcai.org/proceedings/2023/226","pdf":"https://ijcai.org/proceedings/2023/0226.pdf","markdown":"https://ijcai.org/proceedings/2023/226.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/226","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":226,"pages":{"first":2031,"last":2038},"keywords":["Constraint Satisfaction and Optimization: CSO: Solvers and tools"],"videos":[],"references":[{"position":1,"raw":"[Chakraborty et al., 2016] Supratik Chakraborty, Kuldeep S. Meel, and Moshe Y. Vardi. Algorithmic improvements in approximate counting for probabilistic inference: From linear to logarithmic SAT calls. In Proc. of IJCAI, 2016.","title":"Algorithmic improvements in approximate counting for probabilistic inference: From linear to logarithmic SAT calls","authors":"Supratik Chakraborty, Kuldeep S Meel, Moshe Y Vardi","year":"2016","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/503"},{"position":2,"raw":"[Dagum et al., 2000] Paul Dagum, Richard Karp, Michael Luby, and Sheldon Ross. An optimal algorithm for monte carlo estimation. SIAM Journal on computing, 29(5):1484-1496, 2000.","title":"An optimal algorithm for monte carlo estimation","authors":"Paul Dagum, Richard Karp, Michael Luby, Sheldon Ross","year":"2000","venue":"SIAM Journal on computing","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Dalvi and Suciu, 2007] Nilesh N. Dalvi and Dan Suciu. Ef- ficient query evaluation on probabilistic databases. VLDB J., 16(4):523-544, 2007.","title":"Efficient query evaluation on probabilistic databases","authors":"N Nilesh, Dan Dalvi, Suciu","year":"2007","venue":"VLDB J","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Fink and Olteanu, 2011] Robert Fink and Dan Olteanu. On the optimal approximation of queries using tractable propositional languages. In ICDT, pages 174-185, 2011.","title":"On the optimal approximation of queries using tractable propositional languages","authors":"Olteanu Fink, Robert Fink, Dan Olteanu","year":"2011","venue":"ICDT","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Gatterbauer and Suciu, 2014] Wolfgang Gatterbauer and Dan Suciu. Oblivious bounds on the probability of boolean functions. ACM Trans. Database Syst., 39(1):5:1-5:34, 2014.","title":"Oblivious bounds on the probability of boolean functions","authors":"Suciu Gatterbauer, Wolfgang Gatterbauer, Dan Suciu","year":"2014","venue":"ACM Trans. Database Syst","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Gopalan et al., 2013] Parikshit Gopalan, Raghu Meka, and Omer Reingold. DNF sparsification and a faster determin- istic counting algorithm. Comput. Complex., 22(2):275- 310, 2013.","title":"DNF sparsification and a faster deterministic counting algorithm","authors":"Parikshit Gopalan, Raghu Meka, Omer Reingold","year":"2013","venue":"Comput. Complex","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Granlund and the GMP development team, 2020] Torbjörn Granlund and the GMP development team. The GNU multiple precision arithmetic library. Website, Nov 2020. https://gmplib.org/gmp-man-6.2.1.pdf.","title":"Torbjörn Granlund and the GMP development team. The GNU multiple precision arithmetic library","authors":null,"year":"2020","venue":null,"doi":null,"url":"https://gmplib.org/gmp-man-6.2.1.pdf","internal_url":null},{"position":8,"raw":"[Karger, 2001] David R Karger. A Randomized Fully Poly- nomial Time Approximation Scheme for the All-Terminal Network Reliability Problem. SIAM Review, 43(3):499- 522, 2001.","title":"A Randomized Fully Polynomial Time Approximation Scheme for the All-Terminal Network Reliability Problem","authors":"David R Karger","year":"2001","venue":"SIAM Review","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Karp and Luby, 1983] R.M. Karp and M. Luby. Monte- carlo algorithms for enumeration and reliability problems. Proc. of FOCS, 1983.","title":"Montecarlo algorithms for enumeration and reliability problems","authors":"R M Karp, M Luby","year":"1983","venue":"Proc. of FOCS","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Karp et al., 1989] Richard M Karp, Michael Luby, and Neal Madras. Monte-carlo approximation algorithms for enu- meration problems. Journal of Algorithms, 10(3):429 - 448, 1989.","title":"Monte-carlo approximation algorithms for enumeration problems","authors":"Michael Richard M Karp, Neal Luby, Madras","year":"1989","venue":"Journal of Algorithms","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Le Cam, 1960] Lucien Le Cam. An approximation theorem for the poisson binomial distribution. Pacific Journal of Mathematics, 10(4):1181-1197, 1960.","title":"Lucien Le Cam. An approximation theorem for the poisson binomial distribution","authors":"Le Cam","year":"1960","venue":"Pacific Journal of Mathematics","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Luby and Velickovic, 1996] Michael Luby and Boban Velickovic. On deterministic approximation of DNF. Algorithmica, 16(4/5):415-433, 1996.","title":"On deterministic approximation of DNF","authors":"Velickovic Luby, Michael Luby, Boban Velickovic","year":"1996","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Meel et al., 2017] Kuldeep S. Meel, Aditya A. Shrotri, and Moshe Y. Vardi. On hashing-based approaches to approx- imate DNF-counting. In Proc. of FSTTCS, volume 93, pages 41:1-41:14, 2017.","title":"On hashing-based approaches to approximate DNF-counting","authors":"S Kuldeep, Aditya A Meel, Moshe Y Shrotri, Vardi","year":"2017","venue":"Proc. of FSTTCS","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Meel et al., 2019] Kuldeep S. Meel, Aditya A. Shrotri, and Moshe Y. Vardi. Not all FPRASs are equal: demystifying FPRASs for DNF-counting. Constraints An Int. J., 24(3- 4):211-233, 2019.","title":"Not all FPRASs are equal: demystifying FPRASs for DNF-counting","authors":"S Kuldeep, Aditya A Meel, Moshe Y Shrotri, Vardi","year":"2019","venue":"Constraints An Int. J","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Meel et al., 2021] Kuldeep S. Meel, N. V. Vinodchandran, and Sourav Chakraborty. Estimating the size of union of sets in streaming models. In PODS, pages 126-137, 2021.","title":"Estimating the size of union of sets in streaming models","authors":"S Kuldeep, N V Meel, Sourav Vinodchandran, Chakraborty","year":"2021","venue":"PODS","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Olteanu et al., 2010] Dan Olteanu, Jiewen Huang, and Christoph Koch. Approximate confidence computation in probabilistic databases. In ICDE, pages 145-156, 2010.","title":"Approximate confidence computation in probabilistic databases","authors":"Dan Olteanu, Jiewen Huang, Christoph Koch","year":"2010","venue":"ICDE","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Sipser, 1983] Michael Sipser. A complexity theoretic ap- proach to randomness. In STOC, pages 330-335, 1983.","title":"A complexity theoretic approach to randomness","authors":"Michael Sipser","year":"1983","venue":"STOC","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Stockmeyer, 1983] Larry J. Stockmeyer. The complexity of approximate counting (preliminary version). In STOC, pages 118-126, 1983.","title":"The complexity of approximate counting (preliminary version)","authors":"Larry J Stockmeyer","year":"1983","venue":"STOC","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Tao et al., 2004] Qingping Tao, Stephen Donald Scott, N. V. Vinodchandran, and Thomas Takeo Osugi. Svm-based generalized multiple-instance learning via approximate box counting. In ICML, volume 69 of ACM International Conference Proceeding Series. ACM, 2004.","title":"Svm-based generalized multiple-instance learning via approximate box counting","authors":"Qingping Tao, Stephen Donald Scott, N V Vinodchandran, Thomas Takeo Osugi","year":"2004","venue":"ACM International Conference Proceeding Series","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Trevisan, 2004] Luca Trevisan. A note on approximate counting for k-DNF. In APPROX, volume 3122, pages 417-426, 2004.","title":"A note on approximate counting for k-DNF","authors":"Luca Trevisan","year":"2004","venue":"APPROX","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Valiant, 1979] Leslie G. Valiant. The complexity of enu- meration and reliability problems. SIAM Journal on Com- puting, 8(3):410-421, 1979.","title":"The complexity of enumeration and reliability problems","authors":"Leslie G Valiant","year":"1979","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Vazirani, 2001] Vijay V. Vazirani. Approximation algo- rithms. Springer, 2001.","title":"Approximation algorithms","authors":"Vijay V Vazirani","year":"2001","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}