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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.
Models for Advancing PRAM and Other ALgorithms into Parallel Programs For A Pramonchip Platform
"... ..."
Thinking in parallel: Some basic dataparallel algorithms and techniques
 In use as class notes since
, 1993
"... Copyright 19922009, Uzi Vishkin. These class notes reflect the theorertical part in the Parallel ..."
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Cited by 7 (1 self)
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Copyright 19922009, Uzi Vishkin. These class notes reflect the theorertical part in the Parallel
Limits on the Power of Parallel Random Access Machines with Weak Forms of Write Conflict Resolution
, 1993
"... this paper, we use P 1 ; : : : ; P p to denote the p processors of a PRAM and M 1 ; : : : ; Mm to denote its m memory cells. If the input consists of n variables, ..."
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Cited by 5 (1 self)
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this paper, we use P 1 ; : : : ; P p to denote the p processors of a PRAM and M 1 ; : : : ; Mm to denote its m memory cells. If the input consists of n variables,
Uniform Circuits and Exclusive Read PRAMs
 In Proc. of the 11th FST&TCS, number 560 in LNCS
, 1991
"... CRCWPRAMs can be characterized in terms of unbounded fanin circuits. We introduce the notion of SELECTgates. Combining this with the concept of an unambiguous circuit we are able to give a circuit equivalent of EREWPRAMs, thus answering an open question of [SV84]. Moreover, circuits with SELE ..."
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Cited by 3 (0 self)
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CRCWPRAMs can be characterized in terms of unbounded fanin circuits. We introduce the notion of SELECTgates. Combining this with the concept of an unambiguous circuit we are able to give a circuit equivalent of EREWPRAMs, thus answering an open question of [SV84]. Moreover, circuits with SELECTgates characterize CRCW, CREW, ERCW, and EREWPRAMs in a uniform manner. Introduction Parallel random access machines (PRAMs) and uniform circuit families are very important models in parallel complexity theory. Other important models are alternating Turing machines and auxiliary pushdown automata (see e.g. [Ruz80, Coo85]). NC , the class of efficiently parallel solvable problems, can be characterized in terms of all these models. For the design of efficient parallel algorithms, PRAMs are the most favorite model, while circuits are often used to achieve more theoretical results, such as lower bounds (see e.g. [Has86]). NC is in fact a hierarchy of classes that contains in particula...
Pointers versus Arithmetic in PRAMs
 Journal of Computer and System Sciences
, 1996
"... Manipulation of pointers in shared data structures is an important communication mechanism used in many parallel algorithms. Indeed, many fundamental algorithms do essentially nothing else. A Parallel Pointer Machine, (or PPM ) is a parallel model having pointers as its principal data type. PPMs hav ..."
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Cited by 3 (1 self)
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Manipulation of pointers in shared data structures is an important communication mechanism used in many parallel algorithms. Indeed, many fundamental algorithms do essentially nothing else. A Parallel Pointer Machine, (or PPM ) is a parallel model having pointers as its principal data type. PPMs have been characterized as PRAMs obeying two restrictions  first, restricted arithmetic capabilities, and second, the CROW memory access restriction (Concurrent Read, Owner Write, a commonly occurring special case of CREW). We present results concerning the relative power of PPMs (and other arithmetically restricted PRAMs) versus CROW PRAMs having ordinary arithmetic capabilities. First, we prove lower bounds separating PPMs from CROW PRAMs. For example, any stepbystep simulation of an nprocessor CROW PRAM by a PPM requires time \Omega# log log n) per step. Second, we show that this lower bound is tight  we give such a stepbystep simulation using O(log log n) time per step. As a coro...
Parallel Computing: Performance Metrics and Models
, 1995
"... We review the many performance metrics that have been proposed for parallel systems (i.e., program  architecture combinations). These include the many vari ants of speedup, efficiency, and isoefficiency. We give reasons why none of these metrics should be used independent of the run time of the pa ..."
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We review the many performance metrics that have been proposed for parallel systems (i.e., program  architecture combinations). These include the many vari ants of speedup, efficiency, and isoefficiency. We give reasons why none of these metrics should be used independent of the run time of the parallel system. The run time remains the dominant metric and the remaining metrics are important only to the extent they favor systems with better run time. We also lay out the mini mum requirements that a model for parallel computers should meet before it can be considered acceptable. While many models have been proposed, none meets all of these requirements. The BSP and LogP models are considered and the importance of the specifics of the interconnect topology in developing good parallel algorithms pointed out.
Fast Randomized Parallel Methods for Planar Convex Hull Construction
, 1991
"... We present a number of efficient parallel algorithms for constructing 2dimensional convex hulls on a randomized CRCW PRAM. Specifically, we show how to build the convex hull of n presorted points in the plane in O(1) time using O(n log n) work, with nexponential probability, or, alternately, in ..."
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Cited by 2 (1 self)
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We present a number of efficient parallel algorithms for constructing 2dimensional convex hulls on a randomized CRCW PRAM. Specifically, we show how to build the convex hull of n presorted points in the plane in O(1) time using O(n log n) work, with nexponential probability, or, alternately, in O(log n) time using O(n) work, with n exponential probability. We also show how to find the convex hull of n unsorted planar points in in O(log n) time using O(n log h) work, with nexponential probability, where h is the number of edges in the convex hull (h is O(n), but can be as small as O(1)). Our algorithm for unsorted inputs depends on the use of new inplace procedures, that is, procedures that are defined on a subset of elements in the input and that work without reordering the input. In order to achieve our nexponential confidence bounds we use a new parallel technique called failure sweeping. Key words: parallel algorithms, convex hulls, randomization, computational geomet...
On the Power of Some PRAM Models
 Journal of Parallel Algorithms and Applications. Vol
, 1997
"... The focus here is the power of some underexplored CRCW PRAMs, which are strictly more powerful than exclusive write PRAM but strictly less powerful than BSR. We show that some problems can be solved more efficiently in time and/or processor bounds on these models. For example, we show that n linearl ..."
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The focus here is the power of some underexplored CRCW PRAMs, which are strictly more powerful than exclusive write PRAM but strictly less powerful than BSR. We show that some problems can be solved more efficiently in time and/or processor bounds on these models. For example, we show that n linearlyranged integers can be sorted in O(log n= log log n) time with optimal linear work on Sum CRCW PRAM. We also show that the maximum gap problem can be solved within the same resource bounds on Maximum CRCW PRAM. Though some models can be shown to be more powerful than others, some of them appear to have incomparable powers. Keywords: PRAM; BSR; time and processor bounds; simulation; sorting. Classification Categories: F.1.1, F.1.2, F.2.2 1 Preliminaries The focus of this work is on some underexplored Concurrent Read Concurrent Write (CRCW) Parallel Random Access Machine (PRAM) models. These PRAM models differ only in the way of resolving write conflicts. Some of them can be shown to be s...
Parallel String Matching Algorithms
, 1990
"... The string matching problem is one of the most studied problems in computer science. While it is very easily stated and many of the simple algorithms perform very well in practice, numerous works have been published on the subject and research is still very active. In this paper we survey recent ..."
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The string matching problem is one of the most studied problems in computer science. While it is very easily stated and many of the simple algorithms perform very well in practice, numerous works have been published on the subject and research is still very active. In this paper we survey recent results on parallel algorithms for the string matching problem.