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33
A New Parallel Algorithm For The Maximal Independent Set Problem
, 1989
"... 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 EREWprocessors. This is the first deterministic algorithm for the maximal independent set problem (MIS) whose running time is polylogarithmic and whose ..."
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Cited by 35 (2 self)
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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 EREWprocessors. This is the first deterministic algorithm for the maximal independent set problem (MIS) whose running time is polylogarithmic and whose processortime product is optimal up to a polylogarithmic factor.
Parallel Algorithmic Techniques for Combinatorial Computation
 Ann. Rev. Comput. Sci
, 1988
"... this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR8511713, CCR8605353, and CCR8814977, and by DARPA contract N0003984C0165. ..."
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Cited by 29 (3 self)
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this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR8511713, CCR8605353, and CCR8814977, and by DARPA contract N0003984C0165.
An optimal O(log log n) time parallel string matching algorithm
 SIAM J. COMPUT
, 1990
"... An optimal O(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V]. ..."
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Cited by 27 (11 self)
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An optimal O(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V].
A Lower Bound for Parallel String Matching
 SIAM J. Comput
, 1993
"... 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 ..."
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Cited by 25 (13 self)
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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 stringmatching. All are on CRCWPRAM 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 CREWPRAM 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...
Symmetry Breaking for Suffix Tree Construction (Extended Abstract)
"... 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, s ..."
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Cited by 23 (3 self)
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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.
An efficient algorithm for dynamic text indexing
 Proc. of 5th Annual ACMSIAM Symposium on Discrete Algorithms
, 1994
"... 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 occurrenc ..."
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Cited by 20 (0 self)
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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 Online 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 wellstudied 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]).
Finding All Periods and Initial Palindromes of a String in Parallel

, 1991
"... An optimal O(log log n) time CRCWPRAM 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 tim ..."
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Cited by 15 (10 self)
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An optimal O(log log n) time CRCWPRAM 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).
Structural Parallel Algorithmics
, 1991
"... 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 knowledgebase on nonnumerical parallel algorithms can be characterized in a structural way ..."
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Cited by 11 (4 self)
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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 knowledgebase on nonnumerical 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'seye 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...
Efficient String Algorithmics
, 1992
"... 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 sequ ..."
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Cited by 8 (6 self)
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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.
Approximate parameterized matching
 In Proc. 12th European Symposium on Algorithms (ESA
, 2004
"... Abstract Two equal length strings s and s0, over alphabets \Sigma s and \Sigma s0, parameterize match if thereexists a bijection ss: \Sigma s! \Sigma s0, such that ss(s) = s0, where ss(s) is the renaming of each characterof s via ss. Parameterized matching is the problem of finding all parameterize ..."
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Cited by 8 (3 self)
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Abstract Two equal length strings s and s0, over alphabets \Sigma s and \Sigma s0, parameterize match if thereexists a bijection ss: \Sigma s! \Sigma s0, such that ss(s) = s0, where ss(s) is the renaming of each characterof s via ss. Parameterized matching is the problem of finding all parameterized matches of apattern string p in a text t and approximate parameterized matching is the problem of finding,at each location, a bijection ss that maximizes the number of characters that are mapped from p to the appropriate plength substring of t.Parameterized matching was introduced as a model for software duplication detection in software maintenance systems and also has applications in image processing and computationalbiology. For example, approximate parameterized matching models image searching with variable color maps in the presence of errors.We consider the problem for which an error threshold, k, is given and the goal is to find alllocations in t for which there exists a bijection ss which maps p into the appropriate plengthsubstring of t with at most k mismatched mappedelements.We show that (1) the approximate parameterized matching, when  p=t, is equivalent tothe maximum matching problem on graphs, implying that (2) maximum matching is reducible to the approximate parameterized matching with threshold k, up till an O(log t) factor (thiscan be achieved by reducing approximate parameterized matching to the problem by using a binary search on the k's). Given the best known maximum matching algorithms an O(m1.5),where m = p  = t, is implied for approximate parameterized matching. We show that (3) forthe k threshold problem we can do this in O(m + k1.5).Our main result (4) is an O(nk1.5 + mk log m) time algorithm where m = p  and n = t. 1 Introduction In the traditional pattern matching model [11, 19], one seeks exact occurrences of a given pattern pin a text t, i.e. text locations where every text symbol is equal to its corresponding pattern symbol.For two equal length strings