Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained seque...

Abstract. This work presents an experimental comparison of intersection algorithms for sorted sequences, including the recent algorithm of Baeza-Yates. This algorithm performs on average less comparisons than the total number of elements of both inputs (n and m respectively) when n = αm (α> 1). We can find applications of this algorithm on query processing in Web search engines, where large intersections, or differences, must be performed fast. In this work we concentrate in studying the behavior of the algorithm in practice, using for the experiments test data that is close to the actual conditions of its applications. We compare the efficiency of the algorithm with other intersection algorithm and we study different optimizations, showing that the algorithm is more efficient than the alternatives in most cases, especially when one of the sequences is much larger than the other. 1

Parallel computers can do more than simply speed up sequential computations. They are capable of finding solutions that are far better in quality than those obtained by sequential computers. This fact is demonstrated by analyzing sequential and parallel solutions to numerical problems in a real-time paradigm. In this setting, numerical data required to solve a problem are received as input by a computer system, at regular intervals. The computer must process its inputs as soon as they arrive. It must also produce its outputs at regular intervals, as soon as they are available. We show that for some real-time numerical problems a parallel computer can deliver a solution that is significantly more accurate than when computed by a sequential computer. Similar results were derived recently in the areas of real-time optimization and real-time cryptography. Key words and phrases: Parallelism, real-time computation, numerical analysis. This research was supported by the Natural Sciences a...

One of the most compelling illustrations of the power of parallelism is the furniture-moving paradigm. In it, a large item of furniture needs to be moved from one place to another. A single mover, working alone, must take the item apart, move each piece separately, and then reassemble the item at the new location, taking a long time to complete the job. By contrast, four movers can simply lift the item and quickly move it to its new location. Thus, the time required to accomplish the task is reduced by a factor significantly larger than four. This paper describes a computational analog to the furniture-moving paradigm. The computation in question is concerned with transferring a computer file from one computer system to another over an insecure communications channel. The file contains private or sensitive information whose secrecy and integrity need to be maintained. Cryptography is used to obtain a digital signature of the file, thereby protecting its integrity, and the...

The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. However, it was shown recently that a second equally important motivation for using parallel computers exists: Within the paradigm of real-time computation, some classes of problems have the property that a solution to a problem in the class computed in parallel is better than the one obtained on a sequential computer. What constitutes a better solution depends on the problem under consideration. Thus, for optimization problems, `better' means `closer to optimal'. The present paper continues this line of inquiry by exploring another class enjoying the aforementioned property, namely, cryptographic problems in a real-time setting. In this class, `better' means `more secure'. A real-time cryptographic problem is presented for which the parallel solution is significantly better than a sequential one.

) Noga Alon Manuel Blum y Amos Fiat z Sampath Kannan x Moni Naor -- Rafail Ostrovsky k Abstract We describe a procedure which may be helpful to any disorganized carpenter who has a mixed pile of bolts and nuts and wants to find the corresponding pairs of bolts and nuts. The procedure uses our (and the carpenter's) ability to construct efficiently highly expanding graphs. The problem considered is given a collection of n bolts of distinct widths and n nuts such that there is a 1-1 correspondence between the nuts and bolts. The goal is to find for each bolt its corresponding nut by comparing nuts to bolts but not nuts to nuts or bolts to bolts. Our objective is to minimize the number of operations of this kind (as well as the total running time). The problem has a randomized algorithm similar to Quicksort. Our main result is an n(log n) O(1) - Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel and AT & T...

.<F3.783e+05> Given a set of<F3.804e+05> n<F3.783e+05> nuts of distinct widths and a set of<F3.804e+05> n<F3.783e+05> bolts such that each nut corresponds to a unique bolt of the same width, how should we match every nut with its corresponding bolt by comparing nuts with bolts? (No comparison is allowed between two nuts or two bolts.) The problem can be naturally viewed as a variant of the classic sorting problem as follows. Given two lists of<F3.804e+05> n<F3.783e+05> numbers each such that one list is a permutation of the other, how should we sort the lists by comparisons only between numbers in di#erent lists? We give an<F3.804e+05><F3.783e+05><F3.804e+05> O(n<F3.783e+05> log<F3.804e+05><F3.783e+05> n)-time deterministic algorithm for the problem. This is optimal up to a constant factor and answers an open question posed by Alon et al.<F3.695e+05> [Proceedings of the<F3.783e+05><F3.695e+05> 5th Annual ACM-SIAM Symposium on Discrete<F3.783e+05> Algorithms, 1994, pp. 690--696]. Moreov...

. The problem of matching nuts and bolts is the following : Given a collection of n nuts of distinct sizes and n bolts such that there is a oneto -one correspondence between the nuts and the bolts, find for each nut its corresponding bolt. We can only compare nuts to bolts. That is we can neither compare nuts to nuts, nor bolts to bolts. This humble restriction on the comparisons appears to make this problem very hard to solve. In fact, the best deterministic solution to date is due to Alon et al . [1] and takes \Theta(n log 4 n) time. Their solution uses (efficient) graph expanders. In this paper, we give a simpler O(n log 2 n) time algorithm which uses only a simple (and not so efficient) expander. 1 Introduction In [7], page 293, Rawlins posed the following interesting problem : We wish to sort a bag of n nuts and n bolts by size in the dark. We can compare the sizes of a nut and a bolt by attempting to screw one into the other. This operation tells us that either the nut is b...

This paper focuses on the improvement in the quality of computation provided by parallelism. The problem of interest is that of computing the maximum of a nonlinear feedback function in a realtime environment. We show that the solution obtained in parallel is asymptotically better than that computed sequentially. Key words and phrases: Parallelism, real-time computation, nonlinear feedback function, maximization. This research was supported by the Natural Sciences and Engineering Research Council of Canada. 1 1 Introduction The central motivation behind parallelism has always been the speeding up of sequential computations. Recently, another aspect of parallel computation was brought to light. It was shown that under some circumstances it is possible to obtain in parallel solutions to computational problems that are significantly better than any solutions computed sequentially. This phenomenon was demonstrated, in a real-time environment, for problems in combinatorial optimiz...

There has been much work on the following question: given n, how large can a subset of {1,..., n} be that has no arithmetic progressions of length 3. We call such sets 3-free. Most of the work has been asymptotic. In this paper we sketch applications of large 3-free sets, present techniques to find large 3-free sets of {1,..., n} for n ≤ 250, and give empirical results obtained by coding up those techniques. In the sequel we survey the known techniques for finding large 3-free sets of {1,..., n} for large n, discuss variants of them, and give empirical results obtained by coding up those techniques and variants.