A new parallel algorithm for the maximal independent set problem is constructed. It runs in O(log 4 n) time when implemented on a linear number of EREW-processors. This is the first deterministic algorithm for the maximal independent set problem (MIS) whose running time is polylogarithmic and whose processor-time product is optimal up to a polylogarithmic factor.

this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR-85-11713, CCR-86-05353, and CCR-88-14977, and by DARPA contract N00039-84-C-0165.

An optimal O(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V].

This talk presents the derivation of an\Omega\Gamma/28 log m) lower bound on the number of rounds necessary for finding occurrences of a pattern string P [1::m] in a text string T [1::2m] in parallel using m comparisons in each round. The parallel complexity of the string matching problem using p processors for general alphabets follows. 1. Introduction Better and better parallel algorithms have been designed for string-matching. All are on CRCW-PRAM with the weakest form of simultaneous write conflict resolution: all processors which write into the same memory location must write the same value of 1. The best CREW-PRAM algorithms are those obtained from the CRCW algorithms for a logarithmic loss of efficiency. Optimal algorithms have been designed: O(logm) time in [8, 17] and O(log log m) time in [4]. (An optimal algorithm is one with pt = O(n) where t is the time and p is the number of processors used.) Recently, Vishkin [18] developed an optimal O(log m) time algorithm. Unlike...

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. We give several algorithms for suffix tree construction. One of them runs in O(log² n) parallel time and O(n) work for input strings whose characters are drawn from a constant size alphabet.

ABSTRACT Text indexing is one of the fundamental problems of string matching. Indeed, the suffix tree, the central data structure of string matching, was developed as an efficient static text indexer. The text indexing problem is that of building a data structure on a text which allows the occurrences of patterns to be quickly looked up. All previous text indexing schemes have been static in the sense that if the text is modified, the data structure must be rebuilt from scratch. In this paper, we present a first dynamic data structure and algorithms for the On-line Dynamic Text Indexing problem. Our algorithms are based on a novel data structure, the border tree, which exploits string periodicities. 1 Introduction Pattern matching is one of the most well-studied fields in computer science. Problems in this field have very broad applications in many areas of computer science. Elegant and efficient algorithms have been developed for exact pattern matching. (e.g. [4, 9]).

An optimal O(log log n) time CRCW-PRAM algorithm for computing all periods of a string is presented. Previous parallel algorithms compute the period only if it is shorter than half of the length of the string. This algorithm can be used to find all initial palindromes of a string in the same time and processor bounds. Both algorithms are the fastest possible over a general alphabet. We derive a lower bound for finding palindromes by a modification of a previously known lower bound for finding the period of a string [3]. When p processors are available the bounds become \Theta(d n p e + log log d1+p=ne 2p).

The first half of the paper is a general introduction which emphasizes the central role that the PRAM model of parallel computation plays in algorithmic studies for parallel computers. Some of the collective knowledge-base on non-numerical parallel algorithms can be characterized in a structural way. Each structure relates a few problems and technique to one another from the basic to the more involved. The second half of the paper provides a bird's-eye view of such structures for: (1) list, tree and graph parallel algorithms; (2) very fast deterministic parallel algorithms; and (3) very fast randomized parallel algorithms. 1 Introduction Parallelism is a concern that is missing from "traditional" algorithmic design. Unfortunately, it turns out that most efficient serial algorithms become rather inefficient parallel algorithms. The experience is that the design of parallel algorithms requires new paradigms and techniques, offering an exciting intellectual challenge. We note that it had...

Problems involving strings arise in many areas of computer science and have numerous practical applications. We consider several problems from a theoretical perspective and provide efficient algorithms and lower bounds for these problems in sequential and parallel models of computation. In the sequential setting, we present new algorithms for the string matching problem improving the previous bounds on the number of comparisons performed by such algorithms. In parallel computation, we present tight algorithms and lower bounds for the string matching problem, for finding the periods of a string, for detecting squares and for finding initial palindromes.

Abstract. Lower bounds are proven on the parallel-time complexity of several basic functions on the most powerful concurrent-read concurrent-write PRAM with unlimited shared memory and unlimited power of individual processors (denoted by PRIORITY(m)): (1) It is proved that with a number of processors polynomial in n, fi(log n) time is needed for addition, multiplication or bitwise OR of n numbers, when each number has II ’ bits. Hence even the bit complexity (i.e., the time complexity as a function of the total number of bits in the input) is logarithmic in this case. This improves a beautiful result of Meyer auf der Heide and Wigderson [22]. They proved a log n lower bound using Ramsey-type techniques. Using Ramsey theory, it is possible to get an upper bound on the number of bits in the inputs used. However, for the case of polynomially many processors, this upper bound is more than a polynomial in n. (2) An R(log n) lower bound is given for PRIORITY(m) with no” ’ processors on a function with inputs from (0, 11, namely for the functionf(xl,.,x.) = C:‘=, x,a ’ where a is fixed and x, E (0, 1). (3) Finally, by a new efficient simulation of PRIORITY(m) by unbounded fan-in circuits, that with less than exponential number of processors, it is proven a PRIORITY(m) cannot compute PARITY in constant time, and with nO” ’ processors Q(G) time is needed. The simulation technique is of