Simple multi-party set reconciliation
Simple multi-party set reconciliation
复制标题
简单的多方集合对账
作者：
M. Mitzenmacher;R. Pagh
Many distributed cloud-based services use multiple loosely consistent replicas of user information to avoid the high overhead of more tightly coupled synchronization. Periodically, the information must be synchronized, or reconciled. One can place this problem in the theoretical framework of set reconciliation: two parties A1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$A_1$$end{document} and A2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$A_2$$end{document} each hold a set of keys, named S1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_1$$end{document} and S2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_2$$end{document} respectively, and the goal is for both parties to obtain S1∪S2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_1 cup S_2$$end{document}. Typically, set reconciliation is interesting algorithmically when sets are large but the set difference |S1-S2|+|S2-S1|documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$|S_1-S_2|+|S_2-S_1|$$end{document} is small. In this setting the focus is on accomplishing reconciliation efficiently in terms of communication; ideally, the communication should depend on the size of the set difference, and not on the size of the sets. In this paper, we extend recent approaches using Invertible Bloom Lookup Tables (IBLTs) for set reconciliation to the multi-party setting. There are three or more parties A1,A2,…,Andocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$A_1,A_2,ldots ,A_n$$end{document} holding sets of keys S1,S2,…,Sndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_1,S_2,ldots ,S_n$$end{document} respectively, and the goal is for all parties to obtain ∪iSidocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$cup _i S_i$$end{document}. While this could be done by pairwise reconciliations, we seek more effective methods. Our general approach can function even if the number of parties is not exactly known in advance, and with some additional cost can be used to determine which other parties hold missing keys. Our methodology uses network coding techniques in conjunction with IBLTs, allowing efficiency in network utilization along with efficiency obtained by passing messages of size O(|∪iSi-∩iSi|)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$O(|cup _i S_i - cap _i S_i|)$$end{document}. By connecting reconciliation with network coding, we can provide efficient reconciliation methods for a number of natural distributed settings.
Many distributed cloud-based services use multiple loosely consistent replicas of user information to avoid the high overhead of more tightly coupled synchronization. Periodically, the information must be synchronized, or reconciled. One can place this problem in the theoretical framework of set reconciliation: two parties A1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$A_1$$end{document} and A2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$A_2$$end{document} each hold a set of keys, named S1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_1$$end{document} and S2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_2$$end{document} respectively, and the goal is for both parties to obtain S1∪S2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_1 cup S_2$$end{document}. Typically, set reconciliation is interesting algorithmically when sets are large but the set difference |S1-S2|+|S2-S1|documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$|S_1-S_2|+|S_2-S_1|$$end{document} is small. In this setting the focus is on accomplishing reconciliation efficiently in terms of communication; ideally, the communication should depend on the size of the set difference, and not on the size of the sets. In this paper, we extend recent approaches using Invertible Bloom Lookup Tables (IBLTs) for set reconciliation to the multi-party setting. There are three or more parties A1,A2,…,Andocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$A_1,A_2,ldots ,A_n$$end{document} holding sets of keys S1,S2,…,Sndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S_1,S_2,ldots ,S_n$$end{document} respectively, and the goal is for all parties to obtain ∪iSidocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$cup _i S_i$$end{document}. While this could be done by pairwise reconciliations, we seek more effective methods. Our general approach can function even if the number of parties is not exactly known in advance, and with some additional cost can be used to determine which other parties hold missing keys. Our methodology uses network coding techniques in conjunction with IBLTs, allowing efficiency in network utilization along with efficiency obtained by passing messages of size O(|∪iSi-∩iSi|)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$O(|cup _i S_i - cap _i S_i|)$$end{document}. By connecting reconciliation with network coding, we can provide efficient reconciliation methods for a number of natural distributed settings.
影响因子：
1.1
作者：
Zengfeng Huang;K. Yi;Qin Zhang
通讯作者：
Zengfeng Huang;K. Yi;Qin Zhang
用于线性时间构造更密集的基于散列的数据结构的混合超图
DOI：
10.1007/978-3-642-35843-2_31
发表时间：
2013
期刊：
影响因子：
--
作者：
Michael Rink
通讯作者：
Michael Rink