Results 11 
17 of
17
Dispersing Hash Functions
 In Proceedings of the 4th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM ’00), volume 8 of Proceedings in Informatics
, 2000
"... A new hashing primitive is introduced: dispersing hash functions. A family of hash functions F is dispersing if, for any set S of a certain size and random h ∈ F, the expected value of S  − h[S]  is not much larger than the expectancy if h had been chosen at random from the set of all functions ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
A new hashing primitive is introduced: dispersing hash functions. A family of hash functions F is dispersing if, for any set S of a certain size and random h ∈ F, the expected value of S  − h[S]  is not much larger than the expectancy if h had been chosen at random from the set of all functions. We give tight, up to a logarithmic factor, upper and lower bounds on the size of dispersing families. Such families previously studied, for example universal families, are significantly larger than the smallest dispersing families, making them less suitable for derandomization. We present several applications of dispersing families to derandomization (fast element distinctness, set inclusion, and static dictionary initialization). Also, a tight relationship between dispersing families and extractors, which may be of independent interest, is exhibited. We also investigate the related issue of program size for hash functions which are nearly perfect. In particular, we exhibit a dramatic increase in program size for hash functions more dispersing than a random function. 1
A New Tradeoff for Deterministic Dictionaries
, 2000
"... . We consider dictionaries over the universe U = f0; 1g w on a unitcost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the se ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
. We consider dictionaries over the universe U = f0; 1g w on a unitcost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the set stored. This is the rst such data structure to simultaneously achieve query time (log n) o(1) and update time O(2 (log n) c ) for a constant c < 1. 1 Introduction Among the most fundamental data structures is the dictionary. A dictionary stores a subset S of a universe U , oering membership queries of the form \x 2 S?". The result of a membership query is either 'no' or a piece of satellite data associated with x. Updates of the set are supported via insertion and deletion of single elements. Several performance measures are of interest for dictionaries: The amount of space used, the time needed to answer queries, and the time needed to perform updates. The most ecient dictionar...
Compressed String Dictionary Lookup with Edit Distance One
"... Abstract. In this paper we present different solutions for the problem of indexing a dictionary of strings in compressed space. Given a pattern P, the index has to report all the strings in the dictionary having edit distance at most one with P. Our first solution is able to solve queries in (almost ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. In this paper we present different solutions for the problem of indexing a dictionary of strings in compressed space. Given a pattern P, the index has to report all the strings in the dictionary having edit distance at most one with P. Our first solution is able to solve queries in (almost optimal) O(P  + occ) time where occ is the number of strings in the dictionary having edit distance at most one with P. The space complexity of this solution is bounded in terms of the kth order entropy of the indexed dictionary. Our second solution further improves this space complexity at the cost of increasing the query time. 1
On Worst Case RobinHood Hashing
 SIAM J. Computing
, 2004
"... We consider open addressing hashing and implement it by using the Robin Hood strategy; that is, in case of collision, the element that has traveled the farthest can stay in the slot. We hash ∼ αn elements into a table of size n where each probe is independent and uniformly distributed over the tab ..."
Abstract
 Add to MetaCart
We consider open addressing hashing and implement it by using the Robin Hood strategy; that is, in case of collision, the element that has traveled the farthest can stay in the slot. We hash ∼ αn elements into a table of size n where each probe is independent and uniformly distributed over the table, and α<1 is a constant. Let Mn be the maximum search time for any of the elements in the table. We show that with probability tending to one, Mn ∈ [log 2 log n + σ, log 2 log n + τ] for some constants σ, τ depending upon α only. This is an exponential improvement over the maximum search time in case of the standard FCFS (first come first served) collision strategy and virtually matches the performance of multiplechoice hash methods.
Decision Support using Finite Automata and Decision Diagrams
"... This thesis considers the area of constraint programming, more specifically, knowledge compilation for the use in decision support. In particular decision support for configuration problems is considered. The main contributions of the thesis are the following: Decision support on unbounded string do ..."
Abstract
 Add to MetaCart
This thesis considers the area of constraint programming, more specifically, knowledge compilation for the use in decision support. In particular decision support for configuration problems is considered. The main contributions of the thesis are the following: Decision support on unbounded string domains A technique is presented that offers decision support for CSPs that contain variables on unbounded string domains and constraints with regular language membership tests on the string variables. The technique has been implemented and it is empirically shown that the technique can support a realtime response on realworld instances. Comparing decision diagrams We compare acyclic DFAs and MDDs and conclude that the difference between the two in structure as well as in size is negligible. We compare directencoded BDDs with logencoded BDDs and empirically show that a direct encoded BDD is orders of magnitudes larger than a corresponding logencoded BDD. Further the use of ZBDDs
Compressed Matrix Multiplication
"... We present a simple algorithm that approximates the product of nbyn real matrices A and B. Let ABF denote the Frobenius norm of AB, and b be a parameter determining the time/accuracy tradeoff. Given 2wise independent hash functions h1, h2: [n] → [b], and s1, s2: [n] → {−1, +1} the algorith ..."
Abstract
 Add to MetaCart
We present a simple algorithm that approximates the product of nbyn real matrices A and B. Let ABF denote the Frobenius norm of AB, and b be a parameter determining the time/accuracy tradeoff. Given 2wise independent hash functions h1, h2: [n] → [b], and s1, s2: [n] → {−1, +1} the algorithm works by first “compressing ” the matrix product into the polynomial n∑ n∑ p(x) = Aiks1(i) x h1(i) n∑ ⎝ Bkjs2(j) x h2(j) k=1 i=1 Using the fast Fourier transform to compute polynomial multiplication, we can compute c0,..., cb−1 such that ∑ i cixi = (p(x) mod xb) + (p(x) div xb) in time Õ(n2 + nb). An unbiased estimator of (AB)ij with variance at most AB  2 F /b can then be computed as: j=1 Cij = s1(i) s2(j) c (h1(i)+h2(j)) mod b. Our approach also leads to an algorithm for computing AB exactly, with high probability, in time Õ(N + nb) in the case where A and B have at most N nonzero entries, and AB has at most b nonzero entries.