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294
The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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Cited by 630 (15 self)
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other
Boltzmann Samplers For The Random Generation Of Combinatorial Structures
 Combinatorics, Probability and Computing
, 2004
"... This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combina ..."
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Cited by 67 (2 self)
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This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combinatorial class  an object receives a probability essentially proportional to an exponential of its size. As demonstrated here, the resulting algorithms based on realarithmetic operations often operate in linear time. They can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice.
Random sampling of sparse trigonometric polynomials
 Appl. Comput. Harm. Anal
, 2006
"... We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by Basis Pursuit has recently been studied by several authors, ..."
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Cited by 41 (18 self)
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We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by Basis Pursuit has recently been studied by several authors, we provide theoretical results on the success probability of reconstruction via Thresholding and OMP for both a continuous and a discrete probability model for the sampling points. We present numerical experiments, which indicate that usually Basis Pursuit is significantly slower than greedy algorithms, while the recovery rates are very similar.
On the existence of similar sublattices
 Canad. J. Math
, 1999
"... Partial answers are given to two questions. When does a lattice Λ contain a sublattice Λ ′ of index N that is geometrically similar to Λ? When is the sublattice “clean”, in the sense A similarity σ of norm c is a linear map from Rn to Rn such that σu · σv = c u · v for u,v ∈ Rn. Let Λ be an ndimens ..."
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Cited by 30 (8 self)
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Partial answers are given to two questions. When does a lattice Λ contain a sublattice Λ ′ of index N that is geometrically similar to Λ? When is the sublattice “clean”, in the sense A similarity σ of norm c is a linear map from Rn to Rn such that σu · σv = c u · v for u,v ∈ Rn. Let Λ be an ndimensional rational lattice, i.e. u · v ∈ Q for u,v ∈ Λ. A sublattice Λ ′ ⊆ Λ is similar to Λ if σ(Λ) = Λ ′ for some similarity σ of norm c. We also call σ a multiplier of norm c for Λ. The index N = [Λ: Λ ′ ] is c n/2, so if n is odd c must be a square, say c = a 2,
Conjunctive selection conditions in main memory
 In Proc. PODS
, 2002
"... We consider the fundamental operation of applying a compound filtering condition to a set of records. With large main memories available cheaply, systems may choose to keep the data entirely in main memory, in order to improve query and/or update performance. The design of a dataintensive algorithm ..."
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Cited by 26 (2 self)
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We consider the fundamental operation of applying a compound filtering condition to a set of records. With large main memories available cheaply, systems may choose to keep the data entirely in main memory, in order to improve query and/or update performance. The design of a dataintensive algorithm in main memory needs to take into account the architectural characteristics of modern processors, just as a diskbased method needs to consider the physical characteristics of disk devices. An important architectural feature that influences the performance of main memory algorithms is the branch misprediction penalty. We demonstrate that branch misprediction has a substantial impact on the performance of an algorithm for applying selection conditions. We describe a space of “query plans ” that are logically equivalent, but differ in terms of performance due to variations in their branch prediction behavior. We propose a cost model that takes branch prediction into account, and develop a query optimization algorithm that chooses a plan with optimal estimated cost for conjunctive conditions. We also develop an efficient heuristic optimization algorithm. We also show how records can be ordered to further reduce branch misprediction effects.
Asymmetric multiple description lattice vector quantizers
 IEEE Trans. Inf. Theory
, 2002
"... Abstract—We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, a ..."
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Cited by 24 (2 self)
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Abstract—We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, along with a general design procedure. The highrate asymptotic performance of the quantizer is also studied. We evaluate the ratedistortion performance of the quantizer and compare it to known informationtheoretic bounds. The highrate asymptotic analysis is compared to the performance of the quantizer. Index Terms—Cubic lattice, highrate quantization, lattice quantization, multiple descriptions, quantization, source coding, successive refinement, vector quantization. I.
Generalized cluster complexes and Coxeter combinatorics
 Int. Math. Res. Notices
"... and study a simplicial complex ∆m (Φ) associated to a finite root system Φ and a nonnegative integer parameter m. Form = 1, our construction specializes to the (simplicial) ..."
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Cited by 23 (1 self)
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and study a simplicial complex ∆m (Φ) associated to a finite root system Φ and a nonnegative integer parameter m. Form = 1, our construction specializes to the (simplicial)
On universal types
 PROC. ISIT 2004
, 2004
"... We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978 ..."
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Cited by 22 (6 self)
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We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978). We show that the empirical probability distributions of any finite order of two sequences of the same universal type converge, in the variational sense, as the sequence length increases. Consequently, the normalized logarithms of the probabilities assigned by any kth order probability assignment to two sequences of the same universal type, as well as the kth order empirical entropies of the sequences, converge for all k. We study the size of a universal type class, and show that its asymptotic behavior parallels that of the conventional counterpart, with the LZ78 code length playing the role of the empirical entropy. We also estimate the number of universal types for sequences of length n, and show that it is of the form exp((1+o(1))γ n/log n) for a well characterized constant γ. We describe algorithms for enumerating the sequences in a universal type class, and for drawing a sequence from the class with uniform probability. As an application, we consider the problem of universal simulation of individual sequences. A sequence drawn with uniform probability from the universal type class of x n is an optimal simulation of x n in a well defined mathematical sense.
A sequential importance sampling algorithm for generating random graphs with prescribed degrees
, 2006
"... Random graphs with a given degree sequence are a useful model capturing several features absent in the classical ErdősRényi model, such as dependent edges and nonbinomial degrees. In this paper, we use a characterization due to Erdős and Gallai to develop a sequential algorithm for generating a ra ..."
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Cited by 22 (0 self)
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Random graphs with a given degree sequence are a useful model capturing several features absent in the classical ErdősRényi model, such as dependent edges and nonbinomial degrees. In this paper, we use a characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows surprisingly efficient sequential importance sampling. Applications are given, including simulating a biological network and estimating the number of graphs with a given degree sequence. 1. Introduction. Random
UNLABELED (2 + 2)FREE POSETS, ASCENT SEQUENCES AND PATTERN AVOIDING PERMUTATIONS
"... Abstract. We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2 + 2)free posets and a certain class of chord diagrams (or involutions), already appear in the literature. The third one is a class of permutations, defined in terms of a new type of ..."
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Cited by 22 (8 self)
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Abstract. We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2 + 2)free posets and a certain class of chord diagrams (or involutions), already appear in the literature. The third one is a class of permutations, defined in terms of a new type of pattern. An attractive property of these patterns is that, like classical patterns, they are closed under the action of D8, the symmetry group of the square. The fourth class is formed by certain integer sequences, called ascent sequences, which have a simple recursive structure and are shown to encode (2 + 2)free posets, chord diagrams and permutations. Our bijections preserve numerous statistics. We also determine the generating function of these classes of objects, thus recovering a series obtained by Zagier for chord diagrams. That this series also counts (2 + 2)free posets seems to be new. Finally, we characterize the ascent sequences that correspond to permutations avoiding the barred pattern 3¯152¯4, and enumerate those permutations, thus settling a conjecture of Lara Pudwell. 1.