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62
Network Decomposition and Locality in Distributed Computation (Extended Abstract)
, 1989
"... ) Baruch Awerbuch Department of Mathematics and Laboratory for Computer Science M.I.T. Cambridge, MA 02139 Andrew V. Goldberg y Department of Computer Science Stanford University Stanford, CA 94305 Michael Luby z International Computer Science Institute Berkeley, CA 94704 Serge A. Plo ..."
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) Baruch Awerbuch Department of Mathematics and Laboratory for Computer Science M.I.T. Cambridge, MA 02139 Andrew V. Goldberg y Department of Computer Science Stanford University Stanford, CA 94305 Michael Luby z International Computer Science Institute Berkeley, CA 94704 Serge A. Plotkin x Department of Computer Science Stanford University Stanford, CA 94305 May 1989 Abstract We introduce a concept of network decomposition, the essence of which is to partition an arbitrary graph into smalldiameter connected components, such that the graph created by contracting each component into a single node has low chromatic number. We present an efficient distributed algorithm for constructing such a decomposition, and demonstrate its use for design of efficient distributed algorithms. Our method yields new deterministic distributed algorithms for finding a maximal independent set and for (\Delta + 1)coloring of graphs with maximum degree \Delta. These algorithms run...
The String Edit Distance Matching Problems with Moves
, 2006
"... The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smalles ..."
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Cited by 62 (3 self)
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The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smallest edit distance between p and substrings of t. We relax the problem so that (a) we allow an additional operation, namely, substring moves, and (b) we allow approximation of this string edit distance. Our result is a near linear time deterministic algorithm to produce a factor of O(log n log ∗ n) approximation to the string edit distance with moves. This is the first known significantly subquadratic algorithm for a string edit distance problem in which the distance involves nontrivial alignments. Our results are obtained by embedding strings into L1 vector space using a simplified parsing technique we call Edit
Parallel Ear Decomposition Search (EDS) And STNumbering In Graphs
, 1986
"... [LEC67] linear time serial algorithm for testing planarity of graphs uses the linear time serial algorithm of [ET76] for stnumbering. This stnumbering algorithm is based on depthfirst search (DFS). A known conjecture states that DFS, which is a key technique in designing serial algorithms, is n ..."
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Cited by 50 (2 self)
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[LEC67] linear time serial algorithm for testing planarity of graphs uses the linear time serial algorithm of [ET76] for stnumbering. This stnumbering algorithm is based on depthfirst search (DFS). A known conjecture states that DFS, which is a key technique in designing serial algorithms, is not amenable to polylog time parallelism using "around linearly" (or even polynomially) many processors. The first contribution of this paper is a general method for searching efficiently in parallel undirected graphs, called eardecomposition search (EDS). The second contribution demonstrates the applicability of this search method. We present an efficient parallel algorithm for stnumbering in a biconnected graph. The algorithm runs in logarithmic time using a linear number of processors on a concurrentread concurrentwrite (CRCW) PRAM. An efficient parallel algorithm for the problem did not exist before. The problem was not even known to be in NC. 1. Introduction We define the problems ...
Extracting randomness using few independent sources
 In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
, 2004
"... In this work we give the first deterministic extractors from a constant number of weak sources whose entropy rate is less than 1/2. Specifically, for every δ> 0 we give an explicit construction for extracting randomness from a constant (depending polynomially on 1/δ) number of distributions over ..."
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In this work we give the first deterministic extractors from a constant number of weak sources whose entropy rate is less than 1/2. Specifically, for every δ> 0 we give an explicit construction for extracting randomness from a constant (depending polynomially on 1/δ) number of distributions over {0, 1} n, each having minentropy δn. These extractors output n bits, which are 2 −n close to uniform. This construction uses several results from additive number theory, and in particular a recent one by Bourgain, Katz and Tao [BKT03] and of Konyagin [Kon03]. We also consider the related problem of constructing randomness dispersers. For any constant output length m, our dispersers use a constant number of identical distributions, each with minentropy Ω(log n) and outputs every possible mbit string with positive probability. The main tool we use is a variant of the “steppingup lemma ” used in establishing lower bound
Radix Sort For Vector Multiprocessors
 In Proceedings Supercomputing '91
, 1991
"... We have designed a radix sort algorithm for vector multiprocessors and have implemented the algorithm on the CRAY YMP. On one processor of the YMP, our sort is over 5 times faster on large sorting problems than the optimized library sort provided by CRAY Research. On eight processors we achieve a ..."
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Cited by 49 (6 self)
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We have designed a radix sort algorithm for vector multiprocessors and have implemented the algorithm on the CRAY YMP. On one processor of the YMP, our sort is over 5 times faster on large sorting problems than the optimized library sort provided by CRAY Research. On eight processors we achieve an additional speedup of almost 5, yielding a routine over 25 times faster than the library sort. Using this multiprocessor version, we can sort at a rate of 15 million 64bit keys per second. Our sorting algorithm is adapted from a dataparallel algorithm previously designed for a highly parallel Single Instruction Multiple Data (SIMD) computer, the Connection Machine CM2. To develop our version we introduce three general techniques for mapping dataparallel algorithms ontovector multiprocessors. These techniques allow us to fully vectorize and parallelize the algorithm. The paper also derives equations that model the performance of our algorithm on the YMP. These equations are then used t...
Approximate Nearest Neighbors and Sequence Comparison With Block Operations
 IN STOC
, 2000
"... We study sequence nearest neighbors (SNN). Let D be a database of n sequences; we would like to preprocess D so that given any online query sequence Q we can quickly find a sequence S in D for which d(S; Q) d(S; T ) for any other sequence T in D. Here d(S; Q) denotes the distance between sequences ..."
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Cited by 43 (6 self)
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We study sequence nearest neighbors (SNN). Let D be a database of n sequences; we would like to preprocess D so that given any online query sequence Q we can quickly find a sequence S in D for which d(S; Q) d(S; T ) for any other sequence T in D. Here d(S; Q) denotes the distance between sequences S and Q, defined to be the minimum number of edit operations needed to transform one to another (all edit operations will be reversible so that d(S; T ) = d(T; S) for any two sequences T and S). These operations correspond to the notion of similarity between sequences that we wish to capture in a given application. Natural edit operations include character edits (inserts, replacements, deletes etc), block edits (moves, copies, deletes, reversals) and block numerical transformations (scaling by an additive or a multiplicative constant). The SNN problem arises in many applications. We present the first known efficient algorithm for "approximate" nearest neighbor search for sequences with p...
The Accelerated Centroid Decomposition Technique For Optimal Parallel Tree Evaluation In Logarithmic Time
, 1986
"... A new general parallel algorithmic technique for computations on trees is presented. The new technique performs a reduction of the tree expression evaluation problem to list ranking; then, the list ranking provides a schedule for evaluating the tree operations. The technique needs logarithmic tim ..."
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Cited by 43 (3 self)
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A new general parallel algorithmic technique for computations on trees is presented. The new technique performs a reduction of the tree expression evaluation problem to list ranking; then, the list ranking provides a schedule for evaluating the tree operations. The technique needs logarithmic time using an optimal number of processors and has applications to other tree problems. This new technique enables us to systematically order four basic ideas and techniques for parallel algorithms on tree: (1) The list ranking problem. (2) The Euler tour technique on trees. (3) The centroid decomposition technique. (4) The new accelerated centroid decomposition (ACD) technique. 1. Introduction The model of parallel computation used in this paper is the concurrentread exclusivewrite (CREW) parallel random access machine (PRAM). A PRAM employs p synchronous processors all having access to a common memory. A CREW PRAM allows concurrent access by several processors to the same common memo...
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 38 (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.
CommunicationEfficient Parallel Algorithms for Distributed RandomAccess Machines
 Algorithmica
, 1988
"... This paper introduces a model for parallel computation, called the distributed randomaccess machine (DRAM), in which the communication requirements of parallel algorithms can be evaluated. A DRAM is an abstraction of a parallel computer in which memory accesses are implemented by routing messages ..."
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Cited by 37 (2 self)
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This paper introduces a model for parallel computation, called the distributed randomaccess machine (DRAM), in which the communication requirements of parallel algorithms can be evaluated. A DRAM is an abstraction of a parallel computer in which memory accesses are implemented by routing messages through a communication network. A DRAM explicitly models the congestion of messages across cuts of the network. We introduce the notion of a conservative algorithm as one whose communication requirements at each step can be bounded by the congestion of pointers of the input data structure across cuts of a DRAM. We give a simple lemma that shows how to "shortcut" pointers in a data structure so that remote processors can communicate without causing undue congestion. We give O(lg n)step, linearprocessor, linearspace, conservative algorithms for a variety of problems on n node trees, such as computing treewalk numberings, finding the separator of a tree, and evaluating all subexpressions ...
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 30 (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.