{"title":"一种固定维数多面体中积分点计数的多项式时间算法","authors":"A. Barvinok","doi":"10.1109/SFCS.1993.366830","DOIUrl":null,"url":null,"abstract":"We prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d-dimensional Euclidean space. Previously such algorithms were known for dimensions d=1,2,3, and 4 only.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"66 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"453","resultStr":"{\"title\":\"A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed\",\"authors\":\"A. Barvinok\",\"doi\":\"10.1109/SFCS.1993.366830\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d-dimensional Euclidean space. Previously such algorithms were known for dimensions d=1,2,3, and 4 only.<<ETX>>\",\"PeriodicalId\":253303,\"journal\":{\"name\":\"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science\",\"volume\":\"66 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"453\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1993.366830\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1993.366830","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
We prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d-dimensional Euclidean space. Previously such algorithms were known for dimensions d=1,2,3, and 4 only.<>