{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,31]],"date-time":"2024-08-31T00:18:42Z","timestamp":1725063522598},"reference-count":8,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"Abstract<\/jats:title>\n This paper analyses a novel two-step Monte Carlo simulation algorithm to estimate the weighted volume of a polytope of the form \n \n \n \n \n A<\/m:mi>\n \u2062<\/m:mo>\n z<\/m:mi>\n <\/m:mrow>\n \u2264<\/m:mo>\n T<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n \n {Az\\leq T}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. The essential idea is to partition the columns of A<\/jats:italic> into two categories \u2013 a lightweight category and a heavyweight category. Simulation is done in a two-step manner where, for every sample of the lightweight category variables we use multiple samples of the heavyweight category variables. Thus, the heavyweight category variables are oversampled with respect to the lightweight category variables and increasing samples of the heavyweight variables at the expense of the lightweight variables will lead to a more efficient Monte Carlo method. In this paper we present a fast heuristic approximate for estimating the optimal oversampling ratio and substantiate with experimental results which confirm the effectiveness of the method.<\/jats:p>","DOI":"10.1515\/mcma-2024-2011","type":"journal-article","created":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T17:26:50Z","timestamp":1722619610000},"page":"281-297","source":"Crossref","is-referenced-by-count":0,"title":["Optimal oversampling ratio in two-step simulation"],"prefix":"10.1515","volume":"30","author":[{"given":"Srinath R.","family":"Naidu","sequence":"first","affiliation":[{"name":"Department of Computer Science & Information Systems , Birla Institute of Technology and Science , Pilani , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gopalakrishnan","family":"Venkiteswaran","sequence":"additional","affiliation":[{"name":"Department of Computer Science & Information Systems , Birla Institute of Technology and Science , Pilani , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,8,3]]},"reference":[{"key":"2024083008370649303_j_mcma-2024-2011_ref_001","doi-asserted-by":"crossref","unstructured":"J. Cohen,\nTwo algorithms for determining volumes of convex polyhedra,\nJ. Assoc. Comput. Mach. 26 (1979), 401\u2013414.","DOI":"10.1145\/322139.322141"},{"key":"2024083008370649303_j_mcma-2024-2011_ref_002","doi-asserted-by":"crossref","unstructured":"M. Dyer, A. Frieze and R. Kannan,\nA random polynomial-time algorithm for approximate the volume of convex bodies,\nJ. ACM 38 (1991), 1\u201317.","DOI":"10.1145\/102782.102783"},{"key":"2024083008370649303_j_mcma-2024-2011_ref_003","doi-asserted-by":"crossref","unstructured":"J. M. Hammersley and D. C. Handscomb,\nGeneral principles of Monte-Carlo method,\nMonte-Carlo Methods,\nMonogr. Appl. Probab. Statist.,\nSpringer, Dordrecht (1964), 50\u201375.","DOI":"10.1007\/978-94-009-5819-7_5"},{"key":"2024083008370649303_j_mcma-2024-2011_ref_004","doi-asserted-by":"crossref","unstructured":"J. A. G. Jess, K. Kalafala, S. R. Naidu, R. H. J. M. Otten and C. Visweswariah,\nStatistical timing for parametric yield prediction of digital integrated circuits,\nIEEE Trans. Comput.-Aided Des. Integrated Circuits 25 (2006), 2376\u20132392.","DOI":"10.1109\/TCAD.2006.881332"},{"key":"2024083008370649303_j_mcma-2024-2011_ref_005","doi-asserted-by":"crossref","unstructured":"L. Khachiyan,\nThe problem of computing the volume of polytopes is NP-hard,\nUpsekhi Mat. Nauk 44 (1989), 199\u2013200.","DOI":"10.1070\/RM1989v044n03ABEH002136"},{"key":"2024083008370649303_j_mcma-2024-2011_ref_006","doi-asserted-by":"crossref","unstructured":"L. Khachiyan,\nComplexity of polytope volume computation,\nNew Trends in Discrete and Computational Geometry,\nSpringer, Berlin (1993), 91\u2013101.","DOI":"10.1007\/978-3-642-58043-7_5"},{"key":"2024083008370649303_j_mcma-2024-2011_ref_007","doi-asserted-by":"crossref","unstructured":"S. R. Naidu,\nSpeeding up Monte-Carlo simulation for statistical timing analysis for digital integrated circuits,\n20th International Conference on VLSI Design held Jointly with 6th International Conference on Embedded Systems,\nIEEE Press, Piscataway (2007), 265\u2013270.","DOI":"10.1109\/VLSID.2007.147"},{"key":"2024083008370649303_j_mcma-2024-2011_ref_008","doi-asserted-by":"crossref","unstructured":"K. Sita and S. R. Naidu,\nVariation-aware parameter based analog yield optimization methods,\nAnalog Integrated Circuits Signal Process. 99 (2019), 123\u2013132.","DOI":"10.1007\/s10470-018-1319-x"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2011\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2011\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T08:37:27Z","timestamp":1725007047000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2011\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,3]]},"references-count":8,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,6,18]]},"published-print":{"date-parts":[[2024,9,1]]}},"alternative-id":["10.1515\/mcma-2024-2011"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2011","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2024,8,3]]}}}