{"title":"指针跟踪的通信复杂性。熵和抽样的应用","authors":"S. Ponzio, J. Radhakrishnan, Venkatesh Srinivasan","doi":"10.1145/301250.301413","DOIUrl":null,"url":null,"abstract":"The following pointer chasing problem plays a central role in the study of bounded round communication complexity. There are two players A and B. There are two sets of vertices V/sub A/ and V/sub B/ of size n each. Player A is given a function f/sub A/: VA/spl rarr/VB and player B is given a function f/sub B/: VB/spl rarr/VA. In the problem g/sub k/ the players have to determine the vertex reached by applying f/sub A/ and f/sub B/ alternately, k times starting with a fixed vertex v/sub 0//spl isin/V/sub A/. That is, in g/sub 1/, they must determine f/sub A/(v/sub 0/), in g/sub 2/ they must determine f/sub B/(f/sub A/(v/sub 0/)), in g/sub 3/ they must determine f/sub A/(f/sub B/(f/sub A/(v/sub 0/))), and so on.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"108 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"The communication complexity of pointer chasing. Applications of entropy and sampling\",\"authors\":\"S. Ponzio, J. Radhakrishnan, Venkatesh Srinivasan\",\"doi\":\"10.1145/301250.301413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The following pointer chasing problem plays a central role in the study of bounded round communication complexity. There are two players A and B. There are two sets of vertices V/sub A/ and V/sub B/ of size n each. Player A is given a function f/sub A/: VA/spl rarr/VB and player B is given a function f/sub B/: VB/spl rarr/VA. In the problem g/sub k/ the players have to determine the vertex reached by applying f/sub A/ and f/sub B/ alternately, k times starting with a fixed vertex v/sub 0//spl isin/V/sub A/. That is, in g/sub 1/, they must determine f/sub A/(v/sub 0/), in g/sub 2/ they must determine f/sub B/(f/sub A/(v/sub 0/)), in g/sub 3/ they must determine f/sub A/(f/sub B/(f/sub A/(v/sub 0/))), and so on.\",\"PeriodicalId\":432015,\"journal\":{\"name\":\"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)\",\"volume\":\"108 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/301250.301413\",\"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. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/301250.301413","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The communication complexity of pointer chasing. Applications of entropy and sampling
The following pointer chasing problem plays a central role in the study of bounded round communication complexity. There are two players A and B. There are two sets of vertices V/sub A/ and V/sub B/ of size n each. Player A is given a function f/sub A/: VA/spl rarr/VB and player B is given a function f/sub B/: VB/spl rarr/VA. In the problem g/sub k/ the players have to determine the vertex reached by applying f/sub A/ and f/sub B/ alternately, k times starting with a fixed vertex v/sub 0//spl isin/V/sub A/. That is, in g/sub 1/, they must determine f/sub A/(v/sub 0/), in g/sub 2/ they must determine f/sub B/(f/sub A/(v/sub 0/)), in g/sub 3/ they must determine f/sub A/(f/sub B/(f/sub A/(v/sub 0/))), and so on.
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