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562
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
Abstract

Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
A highperformance, portable implementation of the MPI message passing interface standard
 Parallel Computing
, 1996
"... MPI (Message Passing Interface) is a specification for a standard library for message passing that was defined by the MPI Forum, a broadly based group of parallel computer vendors, library writers, and applications specialists. Multiple implementations of MPI have been developed. In this paper, we d ..."
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Cited by 888 (67 self)
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MPI (Message Passing Interface) is a specification for a standard library for message passing that was defined by the MPI Forum, a broadly based group of parallel computer vendors, library writers, and applications specialists. Multiple implementations of MPI have been developed. In this paper, we describe MPICH, unique among existing implementations in its design goal of combining portability with high performance. We document its portability and performance and describe the architecture by which these features are simultaneously achieved. We also discuss the set of tools that accompany the free distribution of MPICH, which constitute the beginnings of a portable parallel programming environment. A project of this scope inevitably imparts lessons about parallel computing, the specification being followed, the current hardware and software environment for parallel computing, and project management; we describe those we have learned. Finally, we discuss future developments for MPICH, including those necessary to accommodate extensions to the MPI Standard now being contemplated by the MPI Forum. 1
3SAT in RTIME(1.32971^n)
, 2003
"... This paper deals with worst case bounds on the NPcomplete 3SAT problem. Using an elegant simple random walk algorithm U. Schöning showed in 1999 that a satisfying assignment for a satisfiable 3SAT formula can be found in O((4/3 \epsilon)^n) expected running time. In 2002 T. Hofmeister, U. Schönin ..."
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This paper deals with worst case bounds on the NPcomplete 3SAT problem. Using an elegant simple random walk algorithm U. Schöning showed in 1999 that a satisfying assignment for a satisfiable 3SAT formula can be found in O((4/3 \epsilon)^n) expected running time. In 2002 T. Hofmeister, U
Hardness of approximating the shortest vector problem in high Lp norms
 In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science. IEEE Computer
"... Abstract. Let p> 1beany fixed real. We show that assuming NP ⊆ RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in ℓp norm within a constant factor. Under the stronger assumption NP ⊆ RTIME(2poly(log n)), we show that there is no polynomialtime (log ..."
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Cited by 91 (3 self)
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Abstract. Let p> 1beany fixed real. We show that assuming NP ⊆ RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in ℓp norm within a constant factor. Under the stronger assumption NP ⊆ RTIME(2poly(log n)), we show that there is no polynomial
Free Bits, PCPs and NonApproximability  Towards Tight Results
, 1996
"... This paper continues the investigation of the connection between proof systems and approximation. The emphasis is on proving tight nonapproximability results via consideration of measures like the "free bit complexity" and the "amortized free bit complexity" of proof systems. ..."
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Cited by 224 (39 self)
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This paper continues the investigation of the connection between proof systems and approximation. The emphasis is on proving tight nonapproximability results via consideration of measures like the "free bit complexity" and the "amortized free bit complexity" of proof systems.
Tensorbased hardness of the shortest vector problem to within almost polynomial factors
 In STOC’07—Proceedings of the 39th Annual ACM Symposium on Theory of Computing
, 2007
"... Abstract: We show that unless NP ⊆ RTIME(2poly(logn)), there is no polynomialtime algorithm approximating the Shortest Vector Problem (SVP) on ndimensional lattices in the ℓp norm (1 ≤ p < ∞) to within a factor of 2 (logn)1−ε for any ε> 0. This improves the previous best factor of 2 (logn)1/ ..."
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Cited by 32 (4 self)
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Abstract: We show that unless NP ⊆ RTIME(2poly(logn)), there is no polynomialtime algorithm approximating the Shortest Vector Problem (SVP) on ndimensional lattices in the ℓp norm (1 ≤ p < ∞) to within a factor of 2 (logn)1−ε for any ε> 0. This improves the previous best factor of 2 (logn)1
Efficient probabilistically checkable proofs and applications to approximation
 In Proceedings of STOC93
, 1993
"... 1 ..."
NPhard Sets are PSuperterse Unless R = NP
, 1992
"... A set A is pterse (psuperterse) if, for all q, it is not possible to answer q queries to A by making only q \Gamma 1 queries to A (any set X). Formally, let PF A qtt be the class of functions reducible to A via a polynomialtime truthtable reduction of norm q, and let PF A qT be the class of ..."
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Cited by 28 (5 self)
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of functions reducible to A via a polynomialtime Turing reduction that makes at most q queries. A set A is pterse if PF A qtt 6` PF A (q\Gamma1)T for all constants q. A is psuperterse if PF A qtt 6` PF X qT for all constants q and sets X . We show that all NPhard sets (under p tt reductions
Results 1  10
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562