Finding succinct ordered minimal perfect hash functions

Seiden, Steven S.; Hirschberg, Daniel S.

doi:10.1016/0020-0190(94)00108-1

Cited by 3 publications

(9 citation statements)

References 10 publications

(18 reference statements)

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“…Our first contribution shows that the approach of [11,22,31] can be used to achieve space for retrieval that is very close to the lower bound:…”

Section: New Contributionsmentioning

confidence: 85%

“…Remark 4 A similar construction (over arbitrary fields GF(q)) was described by Seiden and Hirschberg [31] . However, those authors did not have Calkin's results, and so could not give theoretical bounds on the number m of columns needed.…”

Section: The Basic Retrieval Data Structurementioning

confidence: 94%

“…Theorem 1 For any γ > 0, r = O(log n), and any sufficiently large n there exist data structures for the retrieval problem having the following space and time complexity on a unit cost RAM with free access to a fully random hash function: Our basic data structure and query evaluation algorithm is the same as in [11,22]. The new contribution is to analyze a different construction algorithm (suggested in [31]) that is able to achieve a better space usage. Our analysis needs tools and theorems from linear algebra, while that of [11,22] is based on random graph theory ( [31] provided only experimental results).…”

Section: New Contributionsmentioning

confidence: 99%

“…The new contribution is to analyze a different construction algorithm (suggested in [31]) that is able to achieve a better space usage. Our analysis needs tools and theorems from linear algebra, while that of [11,22] is based on random graph theory ( [31] provided only experimental results). To get a data structure that allows expected linear construction time we devise a new variant of the data structure and query evaluation algorithm, retaining simplicity and non-adaptivity.…”

Section: New Contributionsmentioning

confidence: 99%

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Succinct Data Structures for Retrieval and Approximate Membership (Extended Abstract)

Dietzfelbinger

Pagh

2008

Automata, Languages and Programming

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The retrieval problem is the problem of associating data with keys in a set. Formally, the data structure must store a function f : U → {0, 1} r that has specified values on the elements of a given set S ⊆ U , |S| = n, but may have any value on elements outside S. Minimal perfect hashing makes it possible to avoid storing the set S, but this induces a space overhead of Θ(n) bits in addition to the nr bits needed for function values. In this paper we show how to eliminate this overhead. Moreover, we show that for any k query time O(k) can be achieved using space that is within a factor 1 + e −k of optimal, asymptotically for large n. If we allow logarithmic evaluation time, the additive overhead can be reduced to O(log log n) bits whp. The time to construct the data structure is O(n), expected. A main technical ingredient is to utilize existing tight bounds on the probability of almost square random matrices with rows of low weight to have full row rank. In addition to direct constructions, we point out a close connection between retrieval structures and hash tables where keys are stored in an array and some kind of probing scheme is used. Further, we propose a general reduction that transfers the results on retrieval into analogous results on approximate membership, a problem traditionally addressed using Bloom filters. Again, we show how to eliminate the space overhead present in previously known methods, and get arbitrarily close to the lower bound. The evaluation procedures of our data structures are extremely simple (similar to a Bloom filter). For the results stated above we assume free access to fully random hash functions. However, we show how to justify this assumption using extra space o(n) to simulate full randomness on a RAM.

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“…Our first contribution shows that the approach of [11,22,31] can be used to achieve space for retrieval that is very close to the lower bound:…”

Section: New Contributionsmentioning

confidence: 85%

Section: The Basic Retrieval Data Structurementioning

confidence: 94%

Section: New Contributionsmentioning

confidence: 99%

Section: New Contributionsmentioning

confidence: 99%

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Succinct Data Structures for Retrieval and Approximate Membership (Extended Abstract)

Dietzfelbinger

Pagh

2008

Automata, Languages and Programming

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“…The hash function is a black box which points to an address if a key is provided. H(k) is the hashing function which transforms key k into the address where the appropriate item sets are stored [13].…”

Section: Direct Hashing and Pruningmentioning

confidence: 99%

Association Rule Generation using Modified Hashing Function

Ramakrishnana¹,

Jyaraj²

2014

IJCA

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Association rule mining is one of the most interesting and challenging task in data mining process. There exists many association rule mining techniques, each having merits and demerits. The main problem that exists in many traditional association rule mining algorithms is that these algorithms need more than one database scan to generate association rules. As scanning the database is a costly operation, algorithms capable of generating association rules with only one scan is the need of the hour. In this paper, a novel algorithm for generating association rules is presented which uses hashing function. This algorithm scans the database only once by utilizing the latest version of priori algorithm, direct hashing algorithm and pruning process. The algorithm discovers set of association rules from frequent k-item sets by computing the frequency of each item set. Then pruning process is applied to minimize the number of item sets generated after scanning the size of the database. Experimental results show that our method is very effective in generating association rules without any collision, leading to very high data accuracy.

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Constructing Minimal Perfect Hash Functions Using SAT Technology

Weaver

Heule

2020

AAAI

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Minimal perfect hash functions (MPHFs) are used to provide efficient access to values of large dictionaries (sets of key-value pairs). Discovering new algorithms for building MPHFs is an area of active research, especially from the perspective of storage efficiency. The information-theoretic limit for MPHFs is 1/ln 2 ≈ 1.44 bits per key. The current best practical algorithms range between 2 and 4 bits per key. In this article, we propose two SAT-based constructions of MPHFs. Our first construction yields MPHFs near the information-theoretic limit. For this construction, current state-of-the-art SAT solvers can handle instances where the dictionaries contain up to 40 elements, thereby outperforming the existing (brute-force) methods. Our second construction uses XORSAT filters to realize a practical approach with long-term storage of approximately 1.83 bits per key.

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Finding succinct ordered minimal perfect hash functions

Cited by 3 publications

References 10 publications

Succinct Data Structures for Retrieval and Approximate Membership (Extended Abstract)

Succinct Data Structures for Retrieval and Approximate Membership (Extended Abstract)

Association Rule Generation using Modified Hashing Function

Constructing Minimal Perfect Hash Functions Using SAT Technology

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