Varun Kanade, Frederik Mallmann-Trenn, Victor Verdugo
{"title":"简短公告:你的图表有多大?","authors":"Varun Kanade, Frederik Mallmann-Trenn, Victor Verdugo","doi":"10.1145/3087801.3087855","DOIUrl":null,"url":null,"abstract":"We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a seed node and is allowed to make queries about neighbours of nodes that have already been seen. In the case of undirected graphs, an estimator of Katzir et al. (2014) based on a sample from the stationary distribution π uses O(1/(||π||2) + davg) queries; we prove that this is tight. In addition, we establish this as a lower bound even when the algorithm is allowed to crawl the graph arbitrarily; the results of Katzir et al. give an upper bound that is worse by a multiplicative factor tmix · log (n).","PeriodicalId":324970,"journal":{"name":"Proceedings of the ACM Symposium on Principles of Distributed Computing","volume":"75 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Brief Announcement: How Large is your Graph?\",\"authors\":\"Varun Kanade, Frederik Mallmann-Trenn, Victor Verdugo\",\"doi\":\"10.1145/3087801.3087855\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a seed node and is allowed to make queries about neighbours of nodes that have already been seen. In the case of undirected graphs, an estimator of Katzir et al. (2014) based on a sample from the stationary distribution π uses O(1/(||π||2) + davg) queries; we prove that this is tight. In addition, we establish this as a lower bound even when the algorithm is allowed to crawl the graph arbitrarily; the results of Katzir et al. give an upper bound that is worse by a multiplicative factor tmix · log (n).\",\"PeriodicalId\":324970,\"journal\":{\"name\":\"Proceedings of the ACM Symposium on Principles of Distributed Computing\",\"volume\":\"75 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the ACM Symposium on Principles of Distributed Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3087801.3087855\",\"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 the ACM Symposium on Principles of Distributed Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3087801.3087855","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a seed node and is allowed to make queries about neighbours of nodes that have already been seen. In the case of undirected graphs, an estimator of Katzir et al. (2014) based on a sample from the stationary distribution π uses O(1/(||π||2) + davg) queries; we prove that this is tight. In addition, we establish this as a lower bound even when the algorithm is allowed to crawl the graph arbitrarily; the results of Katzir et al. give an upper bound that is worse by a multiplicative factor tmix · log (n).