{"title":"Komlós猜想匹配Banaszczyk界的算法","authors":"N. Bansal, D. Dadush, S. Garg","doi":"10.1109/FOCS.2016.89","DOIUrl":null,"url":null,"abstract":"We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((t log n)1/2), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t1/2 log n) bound. Our result also extends to the more general Komlós setting and gives an algorithmic O(log1/2 n) bound.","PeriodicalId":414001,"journal":{"name":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"177 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"57","resultStr":"{\"title\":\"An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound\",\"authors\":\"N. Bansal, D. Dadush, S. Garg\",\"doi\":\"10.1109/FOCS.2016.89\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((t log n)1/2), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t1/2 log n) bound. Our result also extends to the more general Komlós setting and gives an algorithmic O(log1/2 n) bound.\",\"PeriodicalId\":414001,\"journal\":{\"name\":\"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)\",\"volume\":\"177 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"57\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FOCS.2016.89\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FOCS.2016.89","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound
We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((t log n)1/2), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t1/2 log n) bound. Our result also extends to the more general Komlós setting and gives an algorithmic O(log1/2 n) bound.
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