Cores of random r-partite hypergraphs

Botelho, Fabiano C.; Wormald, Nicholas C.; Ziviani, Nívio

doi:10.1016/j.ipl.2011.10.017

Cited by 8 publications

(9 citation statements)

References 22 publications

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“…The design of new hashing methods for static sets of keys is strongly related to the generation of indexes for Information Retrieval systems, since a significant portion of the time is spent in hash operations. We proposed a construction for minimal perfect hash functions that combines theoretical analysis, practical performance, expected linear constructing time and near optimal space consumption for the data structure [23,24,25,26,27,28]. The space consumption for the data structure considering n keys and m = n (m the size of the hash table) ranges from 2.62n to 3.3n bits, and for m = 1.23n it ranges from 1.95n to 2.7n bits.…”

Section: Web Search Enginesmentioning

confidence: 99%

Information and data management at PUC-rio and UFMG

Furtado

Ziviani

2018

Proc. VLDB Endow.

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Section: Web Search Enginesmentioning

confidence: 99%

Information and data management at PUC-rio and UFMG

Furtado

Ziviani

2018

Proc. VLDB Endow.

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“…5 For simplicity, we assume random hash functions here, and for technical reasons we assume that the hashes of each key yield distinct locations; hence the k hashes yield a uniform subset of k distinct cells from the m k possibilities. Alternatively, this could easily be accomplished, for instance, by splitting the table into k subtables and having the ith hash function choose a location independently and uniformly at random in the ith subtable, which would not asymptotically change the thresholds [4].…”

Section: Review: the 2-party Settingmentioning

confidence: 99%

“…While the theory set reconciliation among two parties has been widely studied, there appears to be no substantial prior work (that we are aware of) specifically examining the theory of multi-party reconciliation schemes, although the question of how to implement them was raised in [29]. 4 Special cases, such as rumor spreading (see, e.g., [10,12,14,18,22,34]), where one (or more) parties have a single key to share with everyone, have been studied, however.…”

Section: Introductionmentioning

confidence: 99%

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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“…For this reason the proof was not included in this paper. Instead it has been published in a more appropriated forum [9]. For the sake of completeness we present a simplified version of Theorem 3.4 in [9].…”

Section: Expected Number Of Iterations For the Mapping Stepmentioning

confidence: 99%