Dynamic Perfect Hashing: Upper and Lower Bounds

Dietzfelbinger, Martin; Karlin, Anna R.; Mehlhorn, Kurt; Heide, Friedhelm Meyer auf der; Rohnert, Hans; Tarjan, Robert E.

doi:10.1137/s0097539791194094

Cited by 221 publications

(53 citation statements)

References 10 publications

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“…The contribution of this paper is a new hashing scheme called CUCKOO HASHING, which possesses the same theoretical properties as the classic dictionary of Dietzfelbinger et al [10], but is much simpler. The scheme has worst case constant lookup time and amortized expected constant time for updates.…”

Section: Introductionmentioning

confidence: 99%

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Cuckoo hashing

Pagh

Rodler²

2004

Journal of Algorithms

842

297

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Section: Introductionmentioning

confidence: 99%

“…The scheme has worst case constant lookup time and amortized expected constant time for updates. Furthermore, the space usage is roughly 2n words, which should be compared with the 35n words used in [10]. This means that the space usage is similar to that of binary search trees.…”

Section: Introductionmentioning

confidence: 99%

Cuckoo hashing

Pagh

Rodler²

2004

Journal of Algorithms

842

297

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“…Implementation Different ways of implementing hash tables have been extensively studied (e.g., [17,26,27,30,34]). Here we consider a simple approach for optimally implementing a hash table: Suppose we wish to store n elements from U in a data structure so that we can have expected constant look-up complexity.…”

Section: Hash Tablesmentioning

confidence: 99%

Authenticated Hash Tables Based on Cryptographic Accumulators

2015

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Suppose a client stores n elements in a hash table that is outsourced to an untrusted server. We address the problem of authenticating the hash table operations, where the goal is to design protocols capable of verifying the correctness of queries and updates performed by the server, thus ensuring the integrity of the remotely stored data across its entire update history. Solutions to this authentication problem allow the client to gain trust in the operations performed by a faulty or even malicious server that lies outside the administrative control of the client. We present two novel schemes that implement an authenticated hash table. An authenticated hash table exports the basic hash-table functionality for maintaining a dynamic set of elements, A preliminary version of this paper [44] was presented at the 15th 123 Algorithmica coupled with the ability to provide short cryptographic proofs that a given element is a member or not of the current set. By employing efficient algorithmic constructs and cryptographic accumulators as the core security primitive, our schemes provide constant proof size, constant verification time and sublinear query or update time, strictly improving upon previous approaches. Specifically, in our first scheme which is based on the RSA accumulator, the server is able to construct a (non-)membership proof in constant time and perform updates in O (n log n) time for any fixed constant 0 < < 1. A variation of this scheme achieves a different trade-off, offering constant update time and O(n ) query time. Our second scheme uses an accumulator based on bilinear pairings to achieve O(n ) update time at the server while keeping all other complexities constant. A variation of this scheme achieves O(n log n) time for queries and constant update time. An experimental evaluation of both solutions shows their practicality.

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“…The key to doing so is the realization that, in computing the intersection of two sets, the indices of the nonzero words in their respective full bit-vector representations themselves form sets which are intersected. Representing a set of indices using dynamic perfect hashing [4] gives an O(1) worstcase membership test and permits the members to be enumerated in linear time (since the storage used is linear in the cardinality). Hence the members of an intersection can be found by enumerating those in the smaller set and checking each for membership in the larger.…”

Section: Speeding Up Set Intersectionsmentioning

confidence: 99%

“…) Yellin and Jutla [12] generalized the problem to that of computing the minimal (as in [8]) or maximal sets in the partial order on the distinct sets in F that is induced by the subset relation. They presented an algorithm that built the partial order in O(N 2 / log N ) operations over a dictionary ADT, and observed that universal hashing [3] or the more complex dynamic perfect hashing [4] gave a randomized amortized expected running time of O(1) per ADT operation. In [10] we showed that their worst-case bound was tight, and presented an implementation with a worst-case complexity of (N 2 / log N ) operations, including (in this case) bit-parallel operations on words.…”

Section: Introductionmentioning

confidence: 99%

A Fast Bit-Parallel Algorithm for Computing the Subset Partial Order

Pritchard

1999

Algorithmica

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A given collection of sets has a natural partial order induced by the subset relation. Let the size N of the collection be defined as the sum of the cardinalities of the sets that comprise it. Algorithms have recently been discovered that compute the partial order in worst-case time O (N 2 / log N ). This paper gives implementations of a variant of a previously proposed algorithm which exploit bit-parallel operations on a RAM with (log N )-bit words. One is shown to have a worst-case complexity of O(N 2 log log N / log 2 N ) operations. This is the first known o(N 2 / log N ) worst case or randomized expected running time for this problem.

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Dynamic Perfect Hashing: Upper and Lower Bounds

Cited by 221 publications

References 10 publications

Cuckoo hashing

Cuckoo hashing

Authenticated Hash Tables Based on Cryptographic Accumulators

A Fast Bit-Parallel Algorithm for Computing the Subset Partial Order

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