{"title":"若干装箱问题的概率分析","authors":"N. Karmarkar","doi":"10.1109/SFCS.1982.37","DOIUrl":null,"url":null,"abstract":"We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an excellent agreement between the two. We also explain a certain empirically observed anomaly in the behaviour of the algorithm. Finally we establish that asymptotically perfect packing is possible when input items are drawn from a monotonically decreasing density function.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"62 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"44","resultStr":"{\"title\":\"Probabilistic analysis of some bin-packing problems\",\"authors\":\"N. Karmarkar\",\"doi\":\"10.1109/SFCS.1982.37\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an excellent agreement between the two. We also explain a certain empirically observed anomaly in the behaviour of the algorithm. Finally we establish that asymptotically perfect packing is possible when input items are drawn from a monotonically decreasing density function.\",\"PeriodicalId\":127919,\"journal\":{\"name\":\"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)\",\"volume\":\"62 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1982-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"44\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1982.37\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1982.37","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Probabilistic analysis of some bin-packing problems
We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an excellent agreement between the two. We also explain a certain empirically observed anomaly in the behaviour of the algorithm. Finally we establish that asymptotically perfect packing is possible when input items are drawn from a monotonically decreasing density function.
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