Results 11  20
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91
Algorithms for Graph Partitioning on the Planted Partition Model
, 1999
"... The NPhard graph bisection problem is to partition the nodes of an undirected graph into two equalsized groups so as to minimize the number of edges that cross the partition. The more general graph lpartition problem is to partition the nodes of an undirected graph into l equalsized groups so as ..."
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Cited by 94 (0 self)
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The NPhard graph bisection problem is to partition the nodes of an undirected graph into two equalsized groups so as to minimize the number of edges that cross the partition. The more general graph lpartition problem is to partition the nodes of an undirected graph into l equalsized groups so
unknown title
"... Abstract We derive an expression of the form c ln n + o(ln n) for the diameter of a sparse randomgraph with a specified degree sequence. The result holds a.a.s., assuming certain convergence and supercriticality conditions are met, and is applicable to the classical random graph Gn,pwith np = \Theta ..."
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Abstract We derive an expression of the form c ln n + o(ln n) for the diameter of a sparse randomgraph with a specified degree sequence. The result holds a.a.s., assuming certain convergence and supercriticality conditions are met, and is applicable to the classical random graph Gn,pwith np
Motion Planning Amidst Movable Square Blocks: Push* is NPhard
, 2000
"... We show that a particular pushingblock puzzle is NPhard, settling an open problem posed by O'Rourke et al [2, 4]. The puzzle consists of unit square blocks on an integer lattice. The robot may move horizontally and vertically in order to reach its goal position. Thereby it can push an arbitrar ..."
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Cited by 1 (0 self)
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an arbitrary number of blocks in sequence as long as there is at least one free square ahead. The proof is by reduction from 3Sat. 1 Problem Definition For m; n 2 N consider a rectangular n \Theta mgrid where each position (x; y) 2 f1; : : : ; mg \Theta f1; : : : ; ng is either free (F) or blocked (B) and a
On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)
, 1995
"... We consider the problem of fitting an n \Theta n distance matrix D by a tree metric T . Let " be the distance to the closest tree metric, that is, " = min T fk T; D k1 g. First we present an O(n 2 ) algorithm for finding an additive tree T such that k T; D k1 3", giving the first a ..."
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Cited by 91 (4 self)
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We consider the problem of fitting an n \Theta n distance matrix D by a tree metric T . Let " be the distance to the closest tree metric, that is, " = min T fk T; D k1 g. First we present an O(n 2 ) algorithm for finding an additive tree T such that k T; D k1 3", giving the first
The conjugate gradient method for large sparse matrices on the Intel iPSC/860 Hypercube
, 1994
"... For large sparse unstructured matrices, the critical parts of the Conjugate Gradient method on the iPSC/860 are the interprocessor communications needed for the matrixvector multiplication and the vectorupdates. In this work several implementations are tested and discussed in search for an optima ..."
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Cited by 1 (0 self)
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, the best timings were obtained for a mapping to a square p np \Theta p np grid, where np is...
Global Optimum Protein Threading with Gapped Alignment and Empirical Pair Score Functions
 J. Mol. Biol
, 1996
"... We describe a branchandbound search algorithm for finding the exact global optimum gapped sequencestructure alignment ("threading") between a protein sequence and a protein core or structural model, using an arbitrary amino acid pair score function (e.g., contact potentials, knowledgeba ..."
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Cited by 69 (5 self)
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with many different score functions and threading methodologies; this paper illustrates five from the literature. On a desktop workstation running LISP, we have found the global optimum protein sequencestructure alignment in NPhard search spaces as large as 9:6 \Theta 10 31 , at rates ranging as high
On Pseudorandomness and ResourceBounded Measure
 Theoretical Computer Science
, 1997
"... In this paper we extend a key result of Nisan and Wigderson [17] to the nondeterministic setting: for all ff ? 0 we show that if there is a language in E = DTIME(2 O(n) ) that is hard to approximate by nondeterministic circuits of size 2 ffn , then there is a pseudorandom generator that can be u ..."
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Cited by 41 (3 self)
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be used to derandomize BP \Delta NP (in symbols, BP \Delta NP = NP). By applying this extension we are able to answer some open questions in [14] regarding the derandomization of the classes BP \Delta \Sigma P k and BP \Delta \Theta P k under plausible measure theoretic assumptions. As a consequence
Note on the Complexity of Some Eigenvector Problems
, 1995
"... We consider the computation of eigenvectors x = (x 1 ; : : : ; n) over the integers, where each component x i satisfies jx i j c for a constant c. We address decisional problems in this context, and describe some problems complete for NP, \Theta p 2 , F \Delta p 2 , \Delta p 2 , and \Sigma ..."
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Cited by 4 (1 self)
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We consider the computation of eigenvectors x = (x 1 ; : : : ; n) over the integers, where each component x i satisfies jx i j c for a constant c. We address decisional problems in this context, and describe some problems complete for NP, \Theta p 2 , F \Delta p 2 , \Delta p 2
A ThreeDimensional Approach to Parallel Matrix Multiplication
 IBM Journal of Research and Development
, 1995
"... A threedimensional (3D) matrix multiplication algorithm for massively parallel processing systems is presented. The P processors are configured as a "virtual" processing cube with dimensions p 1 , p 2 , and p 3 proportional to the matrices' dimensionsM , N , and K. Each processor ..."
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Cited by 52 (0 self)
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processor performs a single local matrix multiplication of size M=p 1 \Theta N=p 2 \Theta K=p 3 . Before the local computation can be carried out, each subcube must receive a single submatrix of A and B. After the single matrix multiplication has completed, K=p 3 submatrices of this product must be sent
Locating P/poly Optimally in the Extended Low Hierarchy
, 1993
"... The low hierarchy within NP and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes. We relocate P/poly from the third \Sigmalevel EL P;\Sigma 3 (Balc'azar et al., 1986) to the third \Thetalevel EL P;\Theta 3 of the extended low hier ..."
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Cited by 11 (0 self)
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The low hierarchy within NP and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes. We relocate P/poly from the third \Sigmalevel EL P;\Sigma 3 (Balc'azar et al., 1986) to the third \Thetalevel EL P;\Theta 3 of the extended low
Results 11  20
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91