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691
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2728 (61 self)
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the smallest l 1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP and BOB, including better sparsity, and superresolution. BP has interesting relations to ideas in areas as diverse as illposed problems, in abstract harmonic analysis, total
Retiming Synchronous Circuitry
 ALGORITHMICA
, 1991
"... This paper describes a circuit transformation called retiming in which registers are added at some points in a circuit and removed from others in such a way that the functional behavior of the circuit as a whole is preserved. We show that retiming can be used to transform a given synchronous circui ..."
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Cited by 376 (3 self)
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 E lgV) algorithm for determining an equivalent retimed circuit with the smallest possible clock period. We show that the problem of determining an equivalent retimed circuit with minimum state (total number of registers) is polynomialtime solvable. This result yields a polynomialtime optimal
Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 302 (22 self)
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be the smallest value so that S can be covered by k hyperstrips (resp. hypercylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NPHard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main
Optimal paths for a car that goes both forwards and backwards
 PACIFIC JOURNAL OF MATHEMATICS
, 1990
"... The path taken by a car with a given minimum turning radius has a lower bound on its radius of curvature at each point, but the path has cusps if the car shifts into or out of reverse gear. What is the shortest such path a car can travel between two points if its starting and ending directions are s ..."
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Cited by 279 (0 self)
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give these paths by explicit formula. Calculating the length of each of these paths and selecting the (not necessarily unique) path with smallest length yields a simple algorithm for a shortest path in each case. These optimal paths or geodesies may be described as follows: If C is an arc of a circle
More on Noncommutative Polynomial Identity Testing
"... We continue the study of noncommutative polynomial identity testing initiated by Raz and Shpilka and present efficient algorithms for the following problems in the noncommutative model: Polynomial identity testing: The algorithm gets as an input an arithmetic circuit with the promise that the polyno ..."
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Cited by 10 (0 self)
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branching programs: The algorithm gets as an input an algebraic branching program (ABP) and outputs a smallest equivalent ABP. The algorithm is based on Nisan’s characterization of ABP complexity, and uses as a subroutine an algorithm for computing linear dependencies amongst arithmetic formulas, a problem
Smallest Equivalent Sets for Finite Propositional Formula Circumscription
, 2000
"... Abstract Circumscription uses classical logic in order to modelize rules with exceptions and implicit knowledge. Formula circumscription is known to be easier to use in order to modelize a situation. We describe when two sets of formulas give the same result, when circumscribed. Two kinds of such eq ..."
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Cited by 1 (1 self)
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, focusing on looking for the smallest possible sets equivalent to a given set, for the two kinds of equivalence. We need to revisit a characterization result of formula circumscription. Then, we are able to describe a way to get all the sets equivalent to a given set, and also a way to get the smallest
The PCP theorem by gap amplification
 In Proceedings of the ThirtyEighth Annual ACM Symposium on Theory of Computing
, 2006
"... The PCP theorem [3, 2] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to [12], has placed the PC ..."
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Cited by 166 (8 self)
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The PCP theorem [3, 2] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to [12], has placed
The largest and the smallest fixed points of permutations
, 904
"... We give a new interpretation of the derangement numbers dn as the sum of the values of the largest fixed points of all nonderangements of length n − 1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We ..."
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We give a new interpretation of the derangement numbers dn as the sum of the values of the largest fixed points of all nonderangements of length n − 1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We
Approximating the Minimum Equivalent Digraph
, 1995
"... The minimum equivalent graph (MEG) problem is as follows: given a directed graph, find a smallest subset of the edges that maintains all teachability relations between nodes. This problem is NPhard; this paper gives an approximation algorithm achieving a performance guarantee of about 1.64 in poly ..."
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Cited by 42 (2 self)
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The minimum equivalent graph (MEG) problem is as follows: given a directed graph, find a smallest subset of the edges that maintains all teachability relations between nodes. This problem is NPhard; this paper gives an approximation algorithm achieving a performance guarantee of about 1
Conformal deformations of the smallest eigenvalue of the ricci tensor
 Max Planck Institute Preprint Nr. 43/2005
, 2005
"... Abstract. We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor to be a constant. It is related to the notion of minimal volumes in comparison geometry. Such a metric with the smallest eigenvalue of the Ricci tensor to be a constant is a ..."
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Cited by 5 (2 self)
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respectively. Define minRicg(x) the smallest eigenvalue of g −1 · Ricg at x ∈ M. Our problem is to find a conformal metric g = e −2u g0 such that (1) min Ricg(x) = constant. It turns out that the problem is equivalent to solving an interesting fully nonlinear uniform elliptic equation. First we recall
Results 1  10
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691