{"type":"ScholarlyArticle","title":"Not All FPRASs are Equal: Demystifying FPRASs for DNF-Counting (Extended Abstract)","authors":[{"name":"Kuldeep S. Meel","slug":"kuldeep-s-meel","given":"Kuldeep S.","family":"Meel","affiliation":"National University of Singapore , Singapore"},{"name":"Aditya A. Shrotri","slug":"aditya-a-shrotri","given":"Aditya A.","family":"Shrotri","affiliation":"Rice University , Houston USA"},{"name":"Moshe Y. Vardi","slug":"moshe-y-vardi","given":"Moshe Y.","family":"Vardi","affiliation":"Rice University , Houston USA"}],"abstract":"The problem of counting the number of solutions of a DNF formula, also called #DNF, is a fundamental problem in AI with wide-ranging applications. Owing to the intractability of the exact variant, efforts have focused on the design of approximate techniques. Consequently, several  Fully Polynomial Randomized Approximation Schemes (FPRASs) based on Monte Carlo techniques have been proposed. Recently, it was discovered that hashing-based techniques too lend themselves to FPRASs for #DNF. Despite significant improvements, the complexity of the hashing-based FPRAS is still worse than that of the best Monte Carlo FPRAS by polylog factors. Two questions were left unanswered in previous works: Can the complexity of the hashing-based techniques be improved? How do these approaches compare empirically? In this paper, we first propose a new search procedure for the hashing-based FPRAS that removes the polylog factors from its time complexity. We then present the first empirical study of runtime behavior of different FPRASs for #DNF, which produces a nuanced picture. We observe that there is no single best algorithm for all formulas and that the algorithm with one of the worst time complexities solves the largest number of benchmarks.","doi":"10.24963/ijcai.2019/865","url":"https://ijcai.org/proceedings/2019/865","pdf":"https://ijcai.org/proceedings/2019/0865.pdf","markdown":"https://ijcai.org/proceedings/2019/865.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/865","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":"Best Sister Conferences","track":"Best Sister Conferences","number":865,"pages":{"first":6211,"last":6215},"keywords":["Constraints and SAT: Constraints: Applications","Constraints and SAT: Constraints: Evaluation and Analysis","Uncertainty in AI: Uncertainty in AI","Constraints and SAT: Other approaches"],"videos":[],"references":[{"position":1,"raw":"[Babai, 1979] L. Babai. Monte-carlo algorithms in graph isomor- phism testing. Université tde Montréal Technical Report, DMS, pages 79-10, 1979.","title":"Monte-carlo algorithms in graph isomorphism testing","authors":"L Babai","year":"1979","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bacchus et al., 2003] F. Bacchus, S. Dalmao, and T. Pitassi. Algo- rithms and complexity results for #SAT and Bayesian inference. In Proc. of FOCS, pages 340-351, 2003.","title":"Algorithms and complexity results for #SAT and Bayesian inference","authors":"F Bacchus, S Dalmao, T Pitassi","year":"2003","venue":"Proc. of FOCS","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Biondi et al., 2018] F. Biondi, M. Enescu, A. Heuser, A. Legay, K. S. Meel, and J. Quilbeuf. Scalable approximation of quantita- tive information flow in programs. In Proc. of VMCAI, 1 2018.","title":"Scalable approximation of quantitative information flow in programs","authors":"F Biondi, M Enescu, A Heuser, A Legay, K S Meel, J Quilbeuf","year":"2018","venue":"Proc. of VMCAI","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Carter and Wegman, 1977] J. L. Carter and M. N. Wegman. Uni- versal classes of hash functions. In Proc. of STOC, pages 106- 112. ACM, 1977.","title":"Universal classes of hash functions","authors":"J L Carter, M N Wegman","year":"1977","venue":"Proc. of STOC","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chakraborty et al., 2016] S. Chakraborty, K. S. Meel, and M. 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":"S Chakraborty, K S Meel, M Y Vardi","year":"2016","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/503"},{"position":6,"raw":"[Dagum et al., 2000] P. Dagum, R. Karp, M. Luby, and S. 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":"P Dagum, R Karp, M Luby, S Ross","year":"2000","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Dalvi and Suciu, 2007] N. Dalvi and D. Suciu. Efficient query evaluation on probabilistic databases. The VLDB Journal, 16(4):523-544, 2007.","title":"Efficient query evaluation on probabilistic databases","authors":"N Dalvi, D Suciu","year":"2007","venue":"The VLDB Journal","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Dueñas-Osorio et al., 2017] L. Dueñas-Osorio, K. S. Meel, R. Paredes, and M. Y. Vardi. SAT-based connectivity reliability estimation for power transmission grids. Technical report, Rice University, 2017.","title":"SAT-based connectivity reliability estimation for power transmission grids","authors":"L Dueñas-Osorio, K S Meel, R Paredes, M Y Vardi","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Ermon et al., 2013] S. Ermon, C. P. Gomes, A. Sabharwal, and B. Selman. Taming the curse of dimensionality: Discrete inte- gration by hashing and optimization. In Proc. of ICML, pages 334-342, 2013.","title":"Taming the curse of dimensionality: Discrete integration by hashing and optimization","authors":"S Ermon, C P Gomes, A Sabharwal, B Selman","year":"2013","venue":"Proc. of ICML","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Karger, 2001] D. R. Karger. A Randomized Fully Polynomial Time Approximation Scheme for the All-Terminal Network Re- liability Problem. SIAM Review, 2001.","title":"A Randomized Fully Polynomial Time Approximation Scheme for the All-Terminal Network Reliability Problem","authors":"D R Karger","year":"2001","venue":"SIAM Review","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Karp and Luby, 1983] R.M. Karp and M. Luby. Monte Carlo algo- rithms for enumeration and reliability problems. Proc. of FOCS, 1983.","title":"Monte Carlo 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":12,"raw":"[Karp et al., 1989] R.M. Karp, M. Luby, and N. Madras. Monte Carlo approximation algorithms for enumeration problems. Jour- nal of Algorithms, 10(3):429-448, 1989.","title":"Monte Carlo approximation algorithms for enumeration problems","authors":"R M Karp, M Luby, N Madras","year":"1989","venue":"Journal of Algorithms","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Meel et al., 2017] K. S. Meel, A. A. Shrotri, and M. Y. Vardi. On hashing-based approaches to approximate DNF-counting. In Proc. of FSTTCS, 12 2017.","title":"On hashing-based approaches to approximate DNF-counting","authors":"K S Meel, A A Shrotri, M Y Vardi","year":"2017","venue":"Proc. of FSTTCS","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Meel et al., 2018] Kuldeep S Meel, Aditya A Shrotri, and Moshe Y Vardi. Not all fprass are equal: demystifying fprass for dnf-counting. Constraints, pages 1-23, 2018.","title":"Not all fprass are equal: demystifying fprass for dnf-counting","authors":"S Kuldeep, Aditya A Meel, Moshe Y Shrotri, Vardi","year":"2018","venue":"Constraints","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Meel, 2018] Kuldeep S Meel. Constrained counting and sampling: Bridging the gap between theory and practice. arXiv preprint arXiv:1806.02239, 2018.","title":"Constrained counting and sampling: Bridging the gap between theory and practice","authors":"S Kuldeep, Meel","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Motwani and Raghavan, 2010] R. Motwani and P. Raghavan. Ran- domized algorithms. 2010.","title":"Randomized algorithms","authors":"R Motwani, P Raghavan","year":"2010","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Valiant, 1979] L.G. Valiant. The complexity of enumeration and reliability problems. SIAM Journal on Computing, 8(3):410-421, 1979.","title":"The complexity of enumeration and reliability problems","authors":"L G Valiant","year":"1979","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Vazirani, 2013] V. V. Vazirani. Approximation algorithms. Springer Science & Business Media, 2013.","title":"Approximation algorithms","authors":"V V Vazirani","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}