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22
Fast Parallel Algorithm for the Maximal Independent Set Problem
 Proc. 16th Annual ACM Symposium on Theory Of Computing
, 1984
"... Abstract. A parallel algorithm is presented that accepts as input a graph G and produces a maximal independent set of vertices in G. On a PRAM without the concurrent write or concurrent read features, the algorithm executes in G((10gn)~) time and uses 0((n/(logn))3) processors, where n is the numbe ..."
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Cited by 93 (1 self)
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Abstract. A parallel algorithm is presented that accepts as input a graph G and produces a maximal independent set of vertices in G. On a PRAM without the concurrent write or concurrent read features, the algorithm executes in G((10gn)~) time and uses 0((n/(logn))3) processors, where n is the number of vertices in G. The algorithm has several novel features that may find other applications. These include the use of balanced incomplete block designs to replace random sampling by deterministic sampling, and the use of a “dynamic pigeonhole principle ” that generalizes the conventional pigeonhole principle.
Constructing as perfect matching is in random NC
, 1986
"... We show that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomialbounded number of processors. We also show that several related problems lie in Random NC. ..."
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Cited by 49 (0 self)
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We show that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomialbounded number of processors. We also show that several related problems lie in Random NC. These include: (i) Constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation; (ii) Constructing a maximumcardinality matching; (iii) Constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary; (iv) Constructing a maximum st flow in a directed graph whose edge weights are given in unary.
Analysis of the binary Euclidean algorithm
 Directions and Recent Results in Algorithms and Complexity
, 1976
"... The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids multiplications and divisions, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. We describe the binary algorithm and consider its average case behaviour. In ..."
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Cited by 33 (2 self)
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The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids multiplications and divisions, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. We describe the binary algorithm and consider its average case behaviour. In particular, we correct some errors in the literature, discuss some recent results of Vallée, and describe a numerical computation which supports a conjecture of Vallée. 1
Global Search Methods For Solving Nonlinear Optimization Problems
, 1997
"... ... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the lear ..."
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Cited by 17 (1 self)
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... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the learning of feedforward neural networks, (b) the design of quadraturemirrorfilter digital filter banks, (c) the satisfiability problem, (d) the maximum satisfiability problem, and (e) the design of multiplierless quadraturemirrorfilter digital filter banks. Our method achieves better solutions than existing methods, or achieves solutions of the same quality but at a lower cost.
A Short History of Computational Complexity
 IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 2002
"... this article mention all of the amazing research in computational complexity theory. We survey various areas in complexity choosing papers more for their historical value than necessarily the importance of the results. We hope that this gives an insight into the richness and depth of this still quit ..."
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Cited by 16 (1 self)
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this article mention all of the amazing research in computational complexity theory. We survey various areas in complexity choosing papers more for their historical value than necessarily the importance of the results. We hope that this gives an insight into the richness and depth of this still quite young eld
Designing visual languages for description logics
 Journal of Logic, Language and Information
"... Semantic networks were developed in cognitive science and artificial intelligence studies as graphical knowledge representation and inference tools emulating human thought processes. Formal analysis of the representation and inference capabilities of the networks modeled them as subsets of standard ..."
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Cited by 8 (6 self)
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Semantic networks were developed in cognitive science and artificial intelligence studies as graphical knowledge representation and inference tools emulating human thought processes. Formal analysis of the representation and inference capabilities of the networks modeled them as subsets of standard firstorder logic (FOL), restricted in the operations allowed in order to ensure the tractability that seemed to characterize human reasoning capabilities. The graphical network representations were modeled as providing a visual language for the logic. Subsets of FOL targeted on knowledge representation came to be called description logics, and research on these logics has focused on issues of tractability of subsets with differing representation capabilities, and on the implementation of practical inference systems achieving the best possible performance. Semantic network research has kept pace with these developments, providing visual languages for knowledge entry, editing, and presenting the results of inference, that translate unambiguously to the underlying description logics. This paper discusses the design issues for such semantic network formalisms, and illustrates them through detailed examples of significant generic knowledge structures analyzed in the literature, including determinables, contrast sets, genus/differentiae, taxonomies, faceted taxonomies, cluster concepts, family resemblances, graded concepts, frames, definitions, rules, rules with exceptions, essence and state assertions, opposites and contraries, relevance, and so on. Such examples provide important test material for any visual language formalism for logic.
A Randomized BSP/CGM Algorithm for the Maximal Independent Set Problem
 PARALLEL PROCESSING LETTERS
, 1999
"... This paper presents a randomized parallel algorithm for the Maximal Independent Set problem. Our algorithm uses a BSPlike computer with p processors and requires that n+m p = \Omega\Gamma p) for a graph with n vertices and m edges. Under this scalability assumption, and after a preprocessing ..."
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Cited by 6 (1 self)
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This paper presents a randomized parallel algorithm for the Maximal Independent Set problem. Our algorithm uses a BSPlike computer with p processors and requires that n+m p = \Omega\Gamma p) for a graph with n vertices and m edges. Under this scalability assumption, and after a preprocessing phase, it computes a maximal independent set after O(log p) communication rounds, with high probability, each round requiring linear computation time O( n+m p ). The preprocessing phase is deterministic and important in order to ensure that degree computations can be implemented efficiently. For this, we give an optimal parallel BSP/CGM algorithm to the pquantiles search problem, which runs in O( m log p p ) time and a constant number of communication rounds, and could be of interest in its own right, as shown in the text.
Evaluating Parallel Algorithms: Theoretical and Practical Aspects
, 1990
"... The motivation for the work reported in this thesis has been to lessen the gap between theory and practice within the eld of parallel computing. When looking for new and faster parallel algorithms for use in massively parallel systems, it is tempting to investigate promising alternatives from the la ..."
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Cited by 5 (4 self)
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The motivation for the work reported in this thesis has been to lessen the gap between theory and practice within the eld of parallel computing. When looking for new and faster parallel algorithms for use in massively parallel systems, it is tempting to investigate promising alternatives from the large body of research done on parallel algorithms within the eld of theoretical computer science. These algorithms are mainly described for the PRAM (Parallel Random Access Machine) model of computation. This thesis proposes a method for evaluating the practical value of PRAM algorithms. The approach is based on implementing PRAM algorithms for execution on a CREW (Concurrent Read Exclusive Write) PRAM simulator. Measuring and analysis of implemented algorithms on nite problems provide new and more practically oriented results than those traditionally obtained by asymptotical analysis (Onotation). The evaluation method is demonstrated by investigating the practical value of a new and important parallel sorting algorithm from theoretical
Parallel algorithms for depthfirst search
, 1991
"... Parallel Algorithms for DepthFirst Search In this paper we examine parallel algorithms for performing a depthfirst search (DFS) of a directed or undirected graph in sublinear time. this subject is interesting in part because DFS seemed at first to be an inherently sequential process, and for a lo ..."
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Cited by 3 (0 self)
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Parallel Algorithms for DepthFirst Search In this paper we examine parallel algorithms for performing a depthfirst search (DFS) of a directed or undirected graph in sublinear time. this subject is interesting in part because DFS seemed at first to be an inherently sequential process, and for a long time many researchers believed that no such algorithms existed. We survey three seminal papers on the subject. The first one proves that a special case of DFS is (in all likelihood) inherently sequential; the second shows that DFS for planar undirected graphs is in NC; and the third shows that DFS for general undirected graphs is in RNC. We also discuss randomnized algorithms, Pcompleteness and matching, three topics that are essential for understanding and appreciating the results in these papers.
An introduction to heuristic algorithms
"... Abstract. Nowadays computers are used to solve incredibly complex problems. But in order to manage with a problem we should develop an algorithm. Sometimes the human brain is not able to accomplish this task. Moreover, exact algorithms might need centuries to manage with formidable challenges. In su ..."
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Abstract. Nowadays computers are used to solve incredibly complex problems. But in order to manage with a problem we should develop an algorithm. Sometimes the human brain is not able to accomplish this task. Moreover, exact algorithms might need centuries to manage with formidable challenges. In such cases heuristic algorithms that find approximate solutions but have acceptable time and space complexity play indispensable role. In this paper heuristics, their areas of application and the basic underlying ideas are surveyed. We also describe in more detail some modern heuristic techniques, namely Evolutionary Algorithms and Support Vector Machines. 1