Journal ArticleDOI
Storing a Sparse Table with 0(1) Worst Case Access Time
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TLDR
A data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time and is easy to implement.Abstract:
A data structure for representing a set of n items from a umverse of m items, which uses space n + o(n) and accommodates membership queries m constant time is described. Both the data structure and the query algorithm are easy to ~mplement.read more
Citations
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Journal ArticleDOI
Quantum Overlapping Tomography
Jordan Cotler,Frank Wilczek +1 more
TL;DR: The theory of perfect hash families was used in this paper to show that all reduced density matrices of an unknown entangled state can be determined with at most ${e}^{\mathcal{O}(k)}{\mathrm{log}}^{2}(n)$ rounds of parallel measurements.
Book ChapterDOI
Space Efficient Hash Tables with Worst Case Constant Access Time
TL;DR: This is the first dictionary that has worst case constant access time and expected constant update time, works with (1+?) n space, and supports satellite information.
Proceedings ArticleDOI
Backyard Cuckoo Hashing: Constant Worst-Case Operations with a Succinct Representation
TL;DR: In this article, the authors present a dynamic dictionary that uses only O(1 + o(1)) bits, where O(B) is the information-theoretic lower bound for representing a set of size n from a universe of size u.
Posted Content
Dynamic Ordered Sets with Exponential Search Trees
Arne Andersson,Mikkel Thorup +1 more
TL;DR: This work introduces exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures, leading to an optimal bound of O(√log n/log log n) for searching and updating a dynamic set X of n integer keys in linear space.
Book ChapterDOI
Efficient Minimal Perfect Hashing in Nearly Minimal Space
Torben Hagerup,Torsten Tholey +1 more
TL;DR: In this paper, the authors considered the problem of constructing a minimal perfect hash function for a subset S of size n of a universe {0,..., u-1}, where the parameters of interest are the space needed to store h, its evaluation time, and the time required to compute h from S to S. The number of bits needed for the representation of h, ignoring the other parameters, has been thoroughly studied and is known to be n log e + log log u ± O(log n), where "log" denotes the binary logarithm.
References
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Journal ArticleDOI
Should Tables Be Sorted
TL;DR: It is shown that, in a rather general model including al1 the commonly-used schemes, $\lceil $ lg(n+l) $\rceil$ probes to the table are needed in the worst case, provided the key space is sufficiently large.
Journal ArticleDOI
Storing a sparse table
TL;DR: This work proposes a good worst-case method for storing a static table of n entries, each an integer between 0 and N - 1, and analysis shows why a simpler algorithm used for compressing LR parsing tables works so well.
Journal ArticleDOI
Perfect hashing functions: a single probe retrieving method for static sets
TL;DR: A refinement of hashing which allows retrieval of an item in a static table with a single probe is considered, and a rough comparison with ordinary hashing is given which shows that this method can be used conveniently in several practical applications.
Journal ArticleDOI
Reciprocal hashing: a method for generating minimal perfect hashing functions
TL;DR: A method is presented for building minimal perfect hash functions, i.e., functions which allow single probe retrieval from minimally sized tables of identifier sets, and a proof of existence for minimalperfect hash functions of a special type (reciprocal type) is given.