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Applying a Result of Frankl and Rödl to the Construction of Steiner Trees in the Hypercube by
"... Let Q(n) be the ndimensional hypercube, and X a set of points in Q(n). The Steiner problem for the hypercube is to find the smallest number L(n,X) of edges in any subtree of Q(n) which spans X. Let W(k,n) be the set of points in Q(n) having weight k, where we normalize k+1 ≤ n 2. We apply a result ..."
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Let Q(n) be the ndimensional hypercube, and X a set of points in Q(n). The Steiner problem for the hypercube is to find the smallest number L(n,X) of edges in any subtree of Q(n) which spans X. Let W(k,n) be the set of points in Q(n) having weight k, where we normalize k+1 ≤ n 2. We apply a result
New spectral methods for ratio cut partition and clustering
 IEEE TRANS. ON COMPUTERAIDED DESIGN
, 1992
"... Partitioning of circuit netlists is important in many phases of VLSI design, ranging from layout to testing and hardware simulation. The ratio cut objective function [29] has received much attention since it naturally captures both mincut and equipartition, the two traditional goals of partitionin ..."
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Cited by 295 (17 self)
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of partitioning. In this paper, we show that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost. We also demonstrate that fast Lanczostype methods for the sparse symmetric eigenvalue problem are a robust basis
PathFinder: A Negotiationbased Performancedriven Router for FPGAs”, FPGA
, 1995
"... Routing FPGAs is a challenging problem because of the relative scarcity of routing resources, both wires and connection points. This can lead either to slow implementations caused by long wiring paths that avoid congestion or a failure to route all signals. This paper presents PathFinder, a router t ..."
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Cited by 202 (13 self)
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such as Triptych, Xilinx 3000 and meshconnected arrays of FPGAs. The results of routing ISCAS benchmarks on the Triptych FPGA architecture show an average increase of only 4.5% in critical path delay over the optimum delay for a placement. Routes of ISCAS benchmarks on the Xilinx 3000 architecture show a greater
Two Algorithms for NearestNeighbor Search in High Dimensions
, 1997
"... Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems aris ..."
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Cited by 201 (0 self)
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Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems
Subcube Faulttolerance In Hypercubes
 IN INFORMATION AND COMPUTATION 102 (1993), PP. 280–314
, 1993
"... We consider the problem of determining the minimum number of faulty processors, κ(n,m), and of faulty links, λ(n,m), in an ndimensional hypercube computer so that every mdimensional subcube is faulty. Best known lower bounds for κ(n,m) and λ(n,m) are proved, several new recursive inequalities and ..."
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Cited by 11 (2 self)
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We consider the problem of determining the minimum number of faulty processors, κ(n,m), and of faulty links, λ(n,m), in an ndimensional hypercube computer so that every mdimensional subcube is faulty. Best known lower bounds for κ(n,m) and λ(n,m) are proved, several new recursive inequalities
The ASTOOT approach to testing objectoriented programs
 ACM Transactions on Software Engineering
, 1994
"... This article describes a new approach to the unit testing of objectoriented programs, a set of tools based on this approach, and two case studies. In this approach, each test case consists of a tuple of sequences of messages, along with tags indicating whether these sequences should put objects of ..."
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Cited by 182 (1 self)
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of parameters was suffkiently large and likelihood of detecting an error tended to increase up to a threshold value as the parameter range increased. Categories and Subject Descriptors: D.2.1 [Software Engineering]: Requirements/Specificstions—languages; D.2.5 [Software Engineering]: Testing and Debugging
Families of finite sets in which no set is covered by the union of r others
, 1985
"... Let f,(n, k) denote the maximum number of ksubsets of an nset satisfying the condition in the title. It is proved that f,(n,r(t1)+1+d)(n t dl/ lk dl u t for n sufficiently large whenever d = 0,1 or d < r/2 t 2 withJh equality holding iff there exists a Steiner system S(t, r(t 1) + l, n d). ..."
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Cited by 159 (2 self)
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Let f,(n, k) denote the maximum number of ksubsets of an nset satisfying the condition in the title. It is proved that f,(n,r(t1)+1+d)(n t dl/ lk dl u t for n sufficiently large whenever d = 0,1 or d < r/2 t 2 withJh equality holding iff there exists a Steiner system S(t, r(t 1) + l, n d
Load Balancing, Selection and Sorting on the Hypercube
 In Proceedings of the 1989 ACM Symposium on Parallel Algorithms and Architectures
, 1989
"... This paper presents novel load balancing, selection and sorting algorithms for the hypercube with 1port communication. The main result is an algorithm for sorting n values on p processors, SmoothSort, that runs asymptotically faster (in the worst case) than any previously known algorithm over a ..."
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Cited by 28 (4 self)
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This paper presents novel load balancing, selection and sorting algorithms for the hypercube with 1port communication. The main result is an algorithm for sorting n values on p processors, SmoothSort, that runs asymptotically faster (in the worst case) than any previously known algorithm over a
2 source dispersers for n o(1) entropy and Ramsey graphs beating the FranklWilson construction
 In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, 2006. [Bou05] Jean Bourgain. More on the
, 2005
"... The main result of this paper is an explicit disperser for two independent sources on n bits, each of minentropy k = 2 log1−α 0 n, for some small absolute constant α0> 0). Put differently, setting N = 2 n and K = 2 k, we construct an explicit N × N Boolean matrix for which no K × K submatrix is ..."
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Cited by 8 (7 self)
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improving the previous bound of 2Õ(√n) due to Frankl and Wilson [FW81]. We also give a construction of a new independent sources extractor that can extract from a constant number of sources of polynomially small minentropy with exponentially small error. This improves independent sources extractor of Rao
Results 1  10
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