Showing papers by "Andrei Z. Broder published in 1990"

Multilevel adaptive hashing

Abstract: A dictionary is a data structure that allows a sequence of on-line insertions, deletions, and lookup operations for keys drawn from a universe U. Typically the size of the dictionary, n, is much smaller than the size of U, and efficient dictionaries are implemented via various hashing schemes. We present a family of hashing algorithms that allow an implementation of a dictionary that is particularly advantageous when the underlying hardware allows the parallelization of hash function computations and the parallelization of memory reads in different memory banks. In this case, our scheme requires exactly one memory cycle for deletes and lookups and constant expected amortized cost for insertions. We use easy-to-compute hash functions and make no unproven assumptions about their randomness properties, or about any property of the keys. According to our analysis, with the Multilevel Hashing Algorithm it is possible to build a dictionary that is able to answer 20 parallel searches among 64,000 entries in less than 5 ps using relatively inexpensive hardware. *DEC Systems Research Center, 130 Lytton Avenue, Palo Alto, CA 94301.

System with a plurality of hash tables each using different adaptive hashing functions

Abstract: A data processing system and method particularly useful for network address lookup in interconnected local area networks uses a family of hashing algorithms that allow implementation of a dictionary that is particularly advantageous when the underlying hardware allows parallel memory reads in different memory banks. The system and method requires exactly one memory cycle for deletes and lookup and constant expected amortized cost for insertions. The system and method uses easy-to-compute hash functions and makes no unproven assumptions about their randomness properties, or about any property of keys drawn from a universe U. The system and method makes it possible to build a dictionary that is able to answer 20 parallel searches among 64,000 entries in less than 5 μs using relatively inexpensive hardware.

Universal sequences and graph cover times: a short survey

Abstract: Let G be a d-regular graph on n vertices. At each vertex v, let the edges incident with v be given the distinct labels 1,…,d. The labels at the two ends of an edge are not necessarily equal, that is, each edge is labeled twice. A sequence σ in {1,…, d}* is said to traverse G from v if, by starting from v and following the sequence of edge labels σ, one covers all the vertices of G. Let G n,d be a collection of d-regular graphs. A sequence σ is called universal for G n,d if it traverses every graph in G n,d , from every starting point v. For a given family G n,d , the length of the shortest universal sequence for G n,d is denoted U(G n,d )

The cost distribution of clustering in random probing

Abstract: A new approach to the analysis of random probing hashing algorithms is presented. The probability-generating function in closed form for the asymptotic cost of insertion via random probing with secondary clustering is derived. For higher-order clustering, it is shown that all the moments of the probability distribution of the insertion cost exist and are asymptotically equal to the corresponding moments of the cost distribution under uniform hashing. The method in this paper also leads to simple derivations for the expected cost of insertion for random probing with secondary and higher-order clustering.