Multi-party set reconciliation using characteristic polynomials

Boral, Anudhyan; Mitzenmacher, Michael

doi:10.1109/allerton.2014.7028589

Cited by 8 publications

(6 citation statements)

References 17 publications

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“…The XOR operations in the IBLT are also redefined in the multi-ary system correspondingly. The possibility of using characteristic polynomials to reconcile multiple sets is investigated by combining with the gossip protocol in general networks [17].…”

Section: Background and Related Work A Set Reconciliationmentioning

confidence: 99%

MCFsyn: A Multi-Party Set Reconciliation Protocol With the Marked Cuckoo Filter

Luo

Zhao

Rottenstreich³

et al. 2021

IEEE Trans. Parallel Distrib. Syst.

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Section: Background and Related Work A Set Reconciliationmentioning

confidence: 99%

MCFsyn: A Multi-Party Set Reconciliation Protocol With the Marked Cuckoo Filter

Luo

Zhao

Rottenstreich³

et al. 2021

IEEE Trans. Parallel Distrib. Syst.

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“…These ideas have been extended, for example to multi-party reconciliation [8,24]. However, there remain many open problems related to reconciliation of objects beyond sets.…”

Section: Related Workmentioning

confidence: 99%

Reconciling Graphs and Sets of Sets

Mitzenmacher

Morgan

2018

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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We explore a generalization of set reconciliation, where the goal is to reconcile sets of sets. Alice and Bob each have a parent set consisting of s child sets, each containing at most h elements from a universe of size u. They want to reconcile their sets of sets in a scenario where the total number of differences between all of their child sets (under the minimum difference matching between their child sets) is d. We give several algorithms for this problem, and discuss applications to reconciliation problems on graphs, databases, and collections of documents. We specifically focus on graph reconciliation, providing protocols based on set of sets reconciliation for random graphs from G(n, p) and for forests of rooted trees.

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“…Then on the arrival of I(A 3 ) the relay could again determine the set difference between A 1 ∪ A 2 and A 3 and use this to build an IBLT for A 1 ∪ A 2 ∪ A 3 . This repeated decoding and encoding approach is used in [3]. However, this approach requires much more work from the relay, namely a full decoding for each newly received IBLT, which should be avoided in many settings.…”

Section: Combining With Network Codingmentioning

confidence: 99%

“…As users migrate information to cloud storage, the burden of reliability moves to the cloud provider. Thus many cloud vendors such as Amazon [13] and Azure ered using IBLTs for scalable synchronization of transactions 3 [1,20]. Multi-party variations would be potentially useful in the Bitcoin setting, where multiple parties may need to track transactions.…”

Section: Introductionmentioning

confidence: 99%

“…Some preliminary results for multi-party settings, also using the IBLT framework but based on pairwise reconciliations, were provided to us by Goyal and Varghese[21]. Also, after the appearance of this work on the arxiv, multi-party set reconciliation using characteristic polynomials and repeated pairwise reconciliations was examined in[3]; their conclusion is that is while it is possible, it currently seems much less efficient than the methods considered here.…”

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confidence: 99%

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Simple multi-party set reconciliation

Mitzenmacher

Pagh

2017

Distrib. Comput.

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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 A1 and A2 each hold a set of keys, named S1 and S2 respectively, and the goal is for both parties to obtain S1 ∪ S2. Typically, set reconciliation is interesting algorithmically when sets are large but the set difference |S1 − S2| + |S2 − S1| 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, . . . , An holding sets of keys S1, S2, . . . , Sn respectively, and the goal is for all parties to obtain ∪iSi. Whiel 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(| ∪i Si − ∩iSi|). By connecting reconciliation with network coding, we can provide efficient reconciliation methods for a number of natural distributed settings.[8] use multiple loosely consistent replicas of user information because of the high overhead of keeping replicas synchronized at all times. Further, users often retain copies of their information on laptops, tablets, phones and Personal Digital Assistants (PDAs); these devices are often disconnected from cloud storage and thus can diverge from the corresponding copies in the cloud. The situation naturally grows even more complicated when multiple users have access to information, because the number of replicas can increase with the number of users. Periodically, however copies of information objects must be synchronized or reconciled. One can also view the need for reconciliation at a higher level, such as for loosely consistent replicas of large databases that may be used for availability by information providers.This paper focuses on the basic problem of set reconciliation. In the 2-party setting, two parties A 1 and A 2 respectively have (usually very similar) sets S 1 and S 2 , and want to reconcile so both have S 1 ∪ S 2 . Our major contribution is to extend the recent approach to set reconciliation for two parties using Invertible Bloom Lookup Tables (IBLTs) to the multi-party setting, where there are three or more parties holding sets S 1 , S 2 , S 3 , . . . , S n , and the goal is for all parties to obtain ∪ i S i . This could of course be do...

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Multi-party set reconciliation using characteristic polynomials

Cited by 8 publications

References 17 publications

MCFsyn: A Multi-Party Set Reconciliation Protocol With the Marked Cuckoo Filter

MCFsyn: A Multi-Party Set Reconciliation Protocol With the Marked Cuckoo Filter

Reconciling Graphs and Sets of Sets

Simple multi-party set reconciliation

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