{"title":"一种适用于稀疏图和重尾稀疏图的通用无损压缩方法","authors":"Payam Delgosha, V. Anantharam","doi":"10.1109/ISIT45174.2021.9517897","DOIUrl":null,"url":null,"abstract":"Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing universal compression methods for such data. In most applications, the graphical data is sparse, meaning that the number of edges in the graph scales more slowly than $n^{2}$, where $n$ denotes the number of vertices. Although in some applications the number of edges scales linearly with $n$, in others the number of edges is much smaller than $n^{2}$ but appears to scale superlinearly with $n$. We call the former sparse graphs and the latter heavy-tailed sparse graphs. In this paper we introduce a universal lossless compression method which is simultaneously applicable to both classes. We do this by employing the local weak convergence framework for sparse graphs and the sparse graphon framework for heavy-tailed sparse graphs.","PeriodicalId":299118,"journal":{"name":"2021 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A Universal Lossless Compression Method applicable to Sparse Graphs and heavy-tailed Sparse Graphs\",\"authors\":\"Payam Delgosha, V. Anantharam\",\"doi\":\"10.1109/ISIT45174.2021.9517897\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing universal compression methods for such data. In most applications, the graphical data is sparse, meaning that the number of edges in the graph scales more slowly than $n^{2}$, where $n$ denotes the number of vertices. Although in some applications the number of edges scales linearly with $n$, in others the number of edges is much smaller than $n^{2}$ but appears to scale superlinearly with $n$. We call the former sparse graphs and the latter heavy-tailed sparse graphs. In this paper we introduce a universal lossless compression method which is simultaneously applicable to both classes. We do this by employing the local weak convergence framework for sparse graphs and the sparse graphon framework for heavy-tailed sparse graphs.\",\"PeriodicalId\":299118,\"journal\":{\"name\":\"2021 IEEE International Symposium on Information Theory (ISIT)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 IEEE International Symposium on Information Theory (ISIT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT45174.2021.9517897\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 IEEE International Symposium on Information Theory (ISIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT45174.2021.9517897","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Universal Lossless Compression Method applicable to Sparse Graphs and heavy-tailed Sparse Graphs
Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing universal compression methods for such data. In most applications, the graphical data is sparse, meaning that the number of edges in the graph scales more slowly than $n^{2}$, where $n$ denotes the number of vertices. Although in some applications the number of edges scales linearly with $n$, in others the number of edges is much smaller than $n^{2}$ but appears to scale superlinearly with $n$. We call the former sparse graphs and the latter heavy-tailed sparse graphs. In this paper we introduce a universal lossless compression method which is simultaneously applicable to both classes. We do this by employing the local weak convergence framework for sparse graphs and the sparse graphon framework for heavy-tailed sparse graphs.