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We present a simple and e cient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738 761, 1994). The space usage is similar to that of binary search trees, i.e., three words per(More)
We generalize Cuckoo Hashing to d-ary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ε)n memory cells, for any constant ε > 0. Assuming uniform hashing, accessing or deleting table entries takes at most d=O (ln (1/ε)) probes and the expected amortized insertion time is constant. This is the first(More)
A static dictionary is a data structure storing subsets of a finite universe U , answering membership queries. We show that on a unit cost RAM with word size Θ(log |U |), a static dictionary for n-element sets with constant worst case query time can be obtained using B+O(log log |U |)+o(n) bits of storage, where B = dlog2 (|U| n )e is the minimum number of(More)
Approximation of non-linear kernels using random feature mapping has been successfully employed in large-scale data analysis applications, accelerating the training of kernel machines. While previous random feature mappings run in O(ndD) time for $n$ training samples in d-dimensional space and D random feature maps, we propose a novel randomized tensor(More)
A minimal perfect hash function maps a set S of n keys into the set { 0, 1, . . . , n− 1 } bijectively. Classical results state that minimal perfect hashing is possible in constant time using a structure occupying space close to the lower bound of log e bits per element. Here we consider the problem of monotone minimal perfect hashing, in which the(More)
Hashing with linear probing dates back to the 1950s, and is among the most studied algorithms. In recent years it has become one of the most important hash table organizations since it uses the cache of modern computers very well. Unfortunately, previous analyses rely either on complicated and space consuming hash functions, or onthe unrealistic assumption(More)
Motivated by the problems of computing sample covariance matrices, and of transforming a collection of vectors to a basis where they are sparse, we present a simple algorithm that computes an approximation of the product of two <i>n</i>-by-<i>n</i> real matrices <i>A</i> and <i>B</i>. Let ||<i>AB</i>||<sub><i>F</i></sub> denote the Frobenius norm of(More)
It is shown that a static dictionary that offers constant-time access to n elements with w-bit keys and occupies O(n) words of memory can be constructed deterministically in O(n log n) time on a unit-cost RAM with word length w and a standard instruction set including multiplication. Whereas a randomized construction working in linear expected time was(More)
A perfect hash function (PHF) h : U → [0, m − 1] for a key set S is a function that maps the keys of S to unique values. The minimum amount of space to represent a PHF for a given set S is known to be approximately 1.44n/m bits, where n = |S|. In this paper we present new algorithms for construction and evaluation of PHFs of a given set (for m = n and m =(More)