{"title":"在时间O(n log log k)内计算长度为k的最长递增子序列","authors":"M. Crochemore, E. Porat","doi":"10.14236/EWIC/VOCS2008.7","DOIUrl":null,"url":null,"abstract":"We consider the complexity of computing a longest increasing subsequence parameterised by the length of the output. Namely, we show that the maximal length k of an increasing subsequence of a permutation of the set of integers -1, 2,..., n} can be computed in time O(n log log k) in the RAM model, improving the previous 30-year bound of O(n log log k). The optimality of the new bound is an open question.","PeriodicalId":247606,"journal":{"name":"BCS International Academic Conference","volume":"174 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Computing a Longest Increasing Subsequence of Length k in Time O(n log log k)\",\"authors\":\"M. Crochemore, E. Porat\",\"doi\":\"10.14236/EWIC/VOCS2008.7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the complexity of computing a longest increasing subsequence parameterised by the length of the output. Namely, we show that the maximal length k of an increasing subsequence of a permutation of the set of integers -1, 2,..., n} can be computed in time O(n log log k) in the RAM model, improving the previous 30-year bound of O(n log log k). The optimality of the new bound is an open question.\",\"PeriodicalId\":247606,\"journal\":{\"name\":\"BCS International Academic Conference\",\"volume\":\"174 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-09-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"BCS International Academic Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14236/EWIC/VOCS2008.7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"BCS International Academic Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14236/EWIC/VOCS2008.7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computing a Longest Increasing Subsequence of Length k in Time O(n log log k)
We consider the complexity of computing a longest increasing subsequence parameterised by the length of the output. Namely, we show that the maximal length k of an increasing subsequence of a permutation of the set of integers -1, 2,..., n} can be computed in time O(n log log k) in the RAM model, improving the previous 30-year bound of O(n log log k). The optimality of the new bound is an open question.
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