We show that simulating a step of a fetch&add pram model on an erew pram model can be made as efficient as integer sorting. In particular, we present several efficient reductions of the simulation problem to various integer sorting problems. By using some recent algorithms for integer sorting, we get simulation algorithms on crew and erew that take o(n lg n) operations where n is the number of processors in the simulated crcw machine. Previous simulations were using \Theta(n lg n) operations. Some of the more interesting simulation results are obtained by using a bootstrapping technique with a crcw pram algorithm for hashing. 1 Introduction The concurrent-read concurrent-write (crcw) pram programmer's model is commonly used for designing parallel algorithms. On the other hand, the weaker exclusive-write pram models are sometimes considered closer to realization. Therefore, while it is more convenient to design algorithms for the stronger crcw model, an extra effort is sometimes neede...

A hash table is a representation of a set in a linear size data structure that supports constanttime membership queries. We show how to construct a hash table for any given set of n keys in O(lg lg n) parallel time with high probability, using n processors on a weak version of a crcw pram. Our algorithm uses a novel approach of hashing by "oblivious execution" based on probabilistic analysis to circumvent the parity lower bound barrier at the near-logarithmic time level. The algorithm is simple and is sketched by the following: 1. Partition the input set into buckets by a random polynomial of constant degree. 2. For t := 1 to O(lg lg n) do (a) Allocate M t memory blocks, each of size K t . (b) Let each bucket select a block at random, and try to injectively map its keys into the block using a random linear function. Buckets that fail carry on to the next iteration. The crux of the algorithm is a careful a priori selection of the parameters M t and K t . The algorithm uses only O(lg lg...

When can we sort in o(n log n) time? Amir M. Ben-Amram*

There is an upsurge in interest in the Markov model and also more general stationary ergodic stochastic distributions in theoretical computer science community recently, (e.g. see [Vitter,Krishnan,FOCS91], [Karlin,Philips,Raghavan,FOCS92] [Raghavan92]) for use of Markov models for on-line algorithms e.g., cashing and prefetching). Their results used the fact that compressible sources are predictable (and vise versa), and show that on-line algorithms can improve their performance by prediction. Actual page access sequences are in fact somewhat compressible, so their predictive methods can be of benefit. This paper investigates the interesting idea of decreasing computation by using learning in the opposite way, namely to determine the difficulty of prediction. That is, we will approximately learn the input distribution, and then improve the performance of the computation when the input is not too predictable, rather than the reverse. To our knowledge, this is first case of a computational problem where we do not assume any particular fixed input distribution and yet computation is decreased when the input is less predictable, rather than the reverse. We concentrate our investigation on a basic computational problem: sorting and a basic data structure problem: maintaining a priority queue. We present the first known case of sorting and priority queue algorithms whose complexity depends on the binary entropy H ≤ 1 of input keys where assume that input keys are generated from an unknown but arbitrary stationary ergodic source. This is, we assume that each of the input keys can be each arbitrarily long, but have entropy H. Note that H

Suffix trees are the main data-structure in string matching algorithmics. There are several serial algorithms for suffix tree construction which run in linear time, but the number of operations in the only parallel algorithm available, due to Apostolico, Iliopoulos, Landau, Schieber and Vishkin, is proportional to n log n. The algorithm is based on labeling substrings, similar to a classical serial algorithm, with the same operations bound, by Karp, Miller and Rosenberg. We show how to break symmetries that occur in the process of assigning labels using the Deterministic Coin Tossing (DCT) technique, and thereby reduce the number of labeled substrings to linear.

The following two computational problems are studied: Duplicate grouping: Assume that n items are given, each of which is labeled by an integer key from the set 0,..., U � 1 4. Store the items in an array of size n such that items with the same key occupy a contiguous segment of the array. Closest pair: Assume that a multiset of n points in the d-dimensional Euclidean space is given, where d � 1 is a fixed integer. Each point is represented as a d-tuple of integers in the range 0,..., U � 14 Ž or of arbitrary real numbers.. Find a closest pair, i.e., a pair of points whose distance is minimal over all such pairs.

appreciated for their kindness, expert guidance, and meaningful technical discussions. Professor Darko Stefanovic generously donated unlimited computing time on a high quality platform, and additionally gave personal time devoted to many thoughtful discussions.