Showing papers on "Permutation published in 2002"
TL;DR: The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described.
Abstract: Requiring only minimal assumptions for validity, nonparametric permutation testing provides a flexible and intuitive methodology for the statistical analysis of data from functional neuroimaging experiments, at some computational expense. Introduced into the functional neuroimaging literature by Holmes et al. ([1996]: J Cereb Blood Flow Metab 16:7-22), the permutation approach readily accounts for the multiple comparisons problem implicit in the standard voxel-by-voxel hypothesis testing framework. When the appropriate assumptions hold, the nonparametric permutation approach gives results similar to those obtained from a comparable Statistical Parametric Mapping approach using a general linear model with multiple comparisons corrections derived from random field theory. For analyses with low degrees of freedom, such as single subject PET/SPECT experiments or multi-subject PET/SPECT or fMRI designs assessed for population effects, the nonparametric approach employing a locally pooled (smoothed) variance estimate can outperform the comparable Statistical Parametric Mapping approach. Thus, these nonparametric techniques can be used to verify the validity of less computationally expensive parametric approaches. Although the theory and relative advantages of permutation approaches have been discussed by various authors, there has been no accessible explication of the method, and no freely distributed software implementing it. Consequently, there have been few practical applications of the technique. This article, and the accompanying MATLAB software, attempts to address these issues. The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described. Three worked examples from PET and fMRI are presented, with discussion, and comparisons with standard parametric approaches made where appropriate. Practical considerations are given throughout, and relevant statistical concepts are expounded in appendices.
6,530 citations
Patent•
31 May 2002
TL;DR: In this paper, a message passing decoding technique for low density parity check (LDPC) codes and long codewords is described, which allows decoding graph structures which are largely comprised of multiple identical copies of a much smaller graph.
Abstract: Methods and apparatus for decoding codewords using message passing decoding techniques which are particularly well suited for use with low density parity check (LDPC) codes and long codewords are described. The described methods allow decoding graph structures which are largely comprised of multiple identical copies of a much smaller graph. Copies of the smaller graph are subject to a controlled permutation operation to create the larger graph structure. The same controlled permutations are directly implemented to support message passing between the replicated copies of the small graph. Messages corresponding to individual copies of the graph are stored in a memory and accessed in sets, one from each copy of the graph, using a SIMD read or write instruction. The graph permutation operation may be implemented by simply reordering messages, e.g., using a cyclic permutation operation, in each set of messages read out of a message memory so that the messages are passed to processing circuits corresponding to different copies of the small graph.
421 citations
13 Aug 2002
TL;DR: A new class of provably invertible mappings which can mix arithmetic operations (negation, addition, subtraction, multiplication) and boolean operations (not, xor, and, or), are highly efficient, and have desirable cryptographic properties are introduced.
Abstract: Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is small (e.g., n = 8) we can compactly represent any such transformation as a lookup table, but when n is large (e.g., n = 64) we usually have to represent it as a composition of simpler operations such as linear mappings, S-P networks, Feistel structures, etc. Since these cryptographic constructions are often implemented in software on standard microprocessors, we are particularly interested in invertible univariate or multivariate transformations which can be implemented as small compositions of basic machine instructions on 32 or 64 bit words. In this paper we introduce a new class of provably invertible mappings which can mix arithmetic operations (negation, addition, subtraction, multiplication) and boolean operations (not, xor, and, or), are highly efficient, and have desirable cryptographic properties. In particular, we show that for any n the mapping x ? x + (x2 ? C) (mod 2n) is a permutation with a single cycle of length 2n iff both the least significant bit and the third least significant bit in the constant C are 1.
176 citations
17 Sep 2002
TL;DR: By exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, a new 1.375-algorithm for the MIN-SBR problem is designed.
Abstract: Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals, MIN-SBR, the problem of sorting a permutation by a minimum number of reversals. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MIN-SBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, we design a new 1.375-algorithm for the MIN-SBR problem.
157 citations
TL;DR: MRPPs are applied in least absolute distance (LAD) regression, randomized block experimental designs, goodness-of- t tests, and traditional and generalized contingency tables and serve as a nonparametric and versatile alternative tools to many traditional statistical approaches.
Abstract: Three approaches are used to compute p values for the test: exact, resampling, and moment approximations. In the exact test, the distance is computed based on the observed data, then the data are permuted over all possible allocations of the objects in different groups and the distance being computed. The p value is the proportion of the arrangements that have the distance is as extreme or even more extreme than the value of the test statistics. When the number of total objects, N , in the test is large, the exact approach becomes computationally prohibitive. Resampling and moment-approximation approaches make computation manageable; however, the results are not always comparable. MRPPs are applied in least absolute distance (LAD) regression, randomized block experimental designs, goodness-of- t tests, and traditional and generalized contingency tables. MRPP serve as a nonparametric and versatile alternative tools to many traditional statistical approaches. MRPP is a computation-intensive approach that is made possible and practical only as the cost of computation steadily decreases. As a whole, this is a well-written book with an intent to generalize this seemly limited tool to a lot applications. For this book to become more valuable, it should also provide more in-depth coverage of the comparisons of the exact, resampling, and moment-approximation tests beyond just displaying the simulated or computed p values.
148 citations
TL;DR: The computational analysis shows that a small proposed modification (pairwise exchange) improves the error performance of the best existing algorithms almost 50% with negligible CPU time.
90 citations
TL;DR: In this article, the classification up to Wilf equivalence of permutation patterns was thought completed up to length 6, and this result includes the only missing equivalence (546213) ∼ (465213), and for i>n e 7 it was concluded all remaining cases in i>S7.
Abstract: For about 10 years, the classification up to Wilf equivalence of permutation patterns was thought completed up to length 6. In this paper, we establish a new class of Wilf-equivalent permutation patterns, namely, (i>n − 1, i>n − 2, i>n, τ) ∼ (i>n − 2, i>n, i>n − 1, τ) for any τ∈i>Sn−3. In particular, at level i>n e 6, this result includes the only missing equivalence (546213) ∼ (465213), and for i>n e 7 it completes the classification of permutation patterns by settling all remaining cases in i>S7.
89 citations
Patent•
8 Mar 2002TL;DR: In this paper, an interleaver and interleaving method each includes two stages, and is useful in coded orthogonal frequency division multiplexed (COFDM) wireless local area networks.
Abstract: An interleaver and interleaving method each includes two stages, and is useful in coded orthogonal frequency division multiplexed (COFDM) wireless local area networks. A first stage performs a first block permutation and a second stage performs bit order permutation to effectuate a second group permutation. A corresponding de-interleaver does just the opposite at the receiver. A double-buffer version includes writing data into one memory block in a first order while reading data from the second block in a second order, with the first and second orders selected to effectuate the first block permutation.
89 citations
Journal Article•
TL;DR: In this article, the first exact polynomial time algorithm for sorting signed permutations by reversals was proposed, and a 1.375-approximation algorithm was given for the special case of unsigned permutations.
Abstract: Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals, MIN-SBR, the problem of sorting a permutation by a minimum number of reversals. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MIN-SBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, we design a new 1.375-algorithm for the MIN-SBR problem.
78 citations
TL;DR: In this article, a branch and bound algorithm was proposed to solve both the weighted and unweighted permutation flow shop problem with the total flow-time objective, which is known to be NP-hard for m ⩾2.
70 citations
TL;DR: Data-dependent permutations (DDP) are introduced as basic cryptographic primitives to construct fast hardware-oriented ciphers and their application in the cipher CIKS-1 is considered.
Abstract: Data-dependent permutations (DDP) are introduced as basic cryptographic primitives to construct fast hardware-oriented ciphers. Some variants of the DDP operations and their application in the cipher CIKS-1 are considered. A feature of CIKS-1 is the use of both the data-dependent transformation of round subkeys and the key-dependent DDP operations.
11 Sep 2002
TL;DR: An algorithm is proposed that decides whether a given permutation can be sorted using just the number of transpositions indicated by the breakpoint lower-bound, and conjecture that the maximum prefix transposition distance is D(n) = n-?n/4?
Abstract: A transposition is an operation that exchanges two consecutive, adjacent blocks in a permutation. A prefix transposition is a transposition that moves the first element in the permutation. In this work we present the first results on the problem of sorting permutations with the minimum number of prefix transpositions. This problem is a variation of the transposition distance problem, related to genome rearrangements. We present approximation algorithms with performance ratios of 2 and 3. We conjecture that the maximum prefix transposition distance is D(n) = n-?n/4? and present the results of several computational tests that support this. Finally, we propose an algorithm that decides whether a given permutation can be sorted using just the number of transpositions indicated by the breakpoint lower-bound.
TL;DR: It is proved that any Catalan continued fraction is the multivariate generating function of a family of statistics on the 132-avoiding permutations, each consisting of a (possibly infinite) linear combination of the eks.
1 Jan 2002
TL;DR: It is demonstrated that the method described can be applied to all of the presently known classes of uniformly representable permutation polynomials, in particular to the o-polynomials of Glynn and Cherowitzo.
Abstract: We outline the basics for a systematic study of permutation polynomials on finite fields with characteristic 2, which admit a certain uniform representation. We describe a general technique to confirm the permutation property of such polynomials by algebraic calculations with multivariate polynomials over the two-element field. These computations are simple, but so extensive that they have to be done with computer support. We demonstrate that our method can be applied to all of the presently known classes of uniformly representable permutation polynomials, in particular to the o-polynomials of Glynn and Cherowitzo.
IBM1
TL;DR: A suite of space-efficient streaming algorithms for approximating the number of inversions in a permutation and an $\Omega(n)$-space lower bound for deterministic approximate computation for these problems are obtained.
Abstract: (MATH) Inversions are used as a fundamental quantity to measure the sortedness of data, to evaluate different ranking methods for databases, and in the context of rank aggregation. Considering the volume of the data sets in these applications, the data stream model {14, 2] is a natural setting to design efficient algorithms.We obtain a suite of space-efficient streaming algorithms for approximating the number of inversions in a permutation. The best space bound we achieve is $O(\log n \log \log n)$ through a deterministic algorithm. In contrast, we derive an $\Omega(n)$ lower bound for randomized exact computation for this problem; thus approximation is essential.(MATH) We also consider two generalizations of this problem: (1) approximating the number of inversions between two permutations, for which we obtain a randomized $O(\sqrt{n} \log n)$-space algorithm, and (2) approximating the number of inversions in a general list, for which we obtain a randomized $O(\sqrt{n} \log^2 n)$-space two-pass algorithm. In contrast, we derive $\Omega(n)$-space lower bounds for deterministic approximate computation for these problems; thus both randomization and approximation are essential.All our algorithms use only O(log n) time per data item.
TL;DR: In this article, the authors investigated the structure theory of totally disconnected locally compact groups in the context of permutation actions and showed that the theory is self-contained and full proofs are given of all the fundamental results.
Abstract: Willis's structure theory of totally disconnected locally compact groups is investigated in the context of permutation actions. This leads to new interpretations of the basic concepts in the theory and also to new proofs of the fundamental theorems and to several new results. The treatment of Willis's theory is self-contained and full proofs are given of all the fundamental results.
Patent•
26 Feb 2002TL;DR: In this article, a Turbo code interleaver using a number of look-up tables is presented, which includes a storage unit, sets of tables, and an address generator.
Abstract: Techniques to efficiently generate memory addresses for a Turbo code interleaver using a number of look-up tables An interleaver includes a storage unit, sets of tables, and an address generator The storage unit stores K elements for a data packet at locations representative of an RxC array, with the elements being stored in a first (eg, linear) order and provided in a second (eg, interleaved) order A first set of table(s) stores sequences (eg, inter-row permutation sequences PA, PB, PC and PD) used to perform row permutation of the array to map from the first order to the second order A second set of table(s) stores sequences (eg, intra-row base sequences and prime number sequences) used to perform column permutation The address generator receives a first address for the first order and generates a corresponding second address for the second order based on sequences stored in the tables
TL;DR: A permutation array (PA) of length n and minimum distance d is a set of permutations of n elements such that any two permutations coincide in at most n - d positions.
Abstract: A permutation array (PA) of length n and minimum distance d is a set of permutations of n elements such that any two permutations coincide in at most n - d positions. Some constructions of PAs are given.
1 Jan 2002
TL;DR: This work performs computational experiments with four well-known permutation problems to study and compare the performance of a SS and a GA implementation.
Abstract: The purpose of this work is to compare the performance of a scatter search (SS) implementation and an implementation of a genetic algorithm (GA) in the context of searching for optimal solutions to permutation problems. Scatter search and genetic algorithms are members of the evolutionary computation family. That is, they are both based on maintaining a population of solutions for the purpose of generating new trial solutions. We perform computational experiments with four well-known permutation problems to study and compare the performance of a SS and a GA implementation.
TL;DR: The permutations that can be sorted by two stacks in series are considered and a forbidden characterisation of such permutations is obtained, subject to the condition that each stack remains ordered.
TL;DR: An inversion sequence is proposed as the representation of a permutation which allows repetitive values and hence is robust under ordinary (n-point) crossover and is compared to the well known PMX special crossover method.
Abstract: Ordinary representations of permutations in Genetic Algorithms (GA) is handicapped with producing offspring which aze not permutations at all. The conventional solution for crossover and mutation operations of permutations is to device ‘special’ operators. Unfortunately these operators suffer from violating the nature of crossover. Namely, considering the gene positions on the chromosome, these methods do not allow n-point crossover techniques which are known to favour building-block formations. In this work, an inversion sequence is proposed as the representation of a permutation. This sequence allows repetitive values and hence is robust under ordinary (n-point) crossover. There is a one-to-one mapping from ordinary permutation representation to the inversion sequence representation. The proposed method is used for solving TSPs and is compared to the well known PMX special crossover method. It is observed that this method outperforms PMX in convergence rate by a factor which can be as high as 1...
11 Sep 2002
TL;DR: In this article, it was shown that the security loss for general trapdoor permutations is Ω(qhash), where qhash is the number of random oracle queries made by the adversary, and that all the security benefits of the RSA based variants come into effect once f comes from a family of claw-free permutation pairs.
Abstract: The popular random-oracle-based signature schemes, such as Probabilistic Signature Scheme (PSS) and Full Domain Hash (FDH), output a signature of the form 〈f-1(y), pub〉, where y somehow depends on the message signed (and pub) and f is some public trapdoor permutation (typically RSA). Interestingly, all these signature schemes can be proven asymptotically secure for an arbitrary trapdoor permutation f, but their exact security seems to be significantly better for special trapdoor permutations like RSA. This leads to two natural questions: (1) can the asymptotic security analysis be improved with general trapdoor permutations?; and, if not, (2) what general cryptographic assumption on f -- enjoyed by specific functions like RSA -- is "responsible" for the improved security?
We answer both these questions. First, we show that if f is a blackbox trapdoor permutation, then the poor exact security is unavoidable. More specifically, the security loss for general trapdoor permutations is Ω(qhash), where qhash is the number of random oracle queries made by the adversary (which could be quite large). On the other hand, we show that all the security benefits of the RSA-based variants come into effect once f comes from a family of claw-free permutation pairs. Our results significantly narrow the current "gap" between general trapdoor permutations and RSA to the "gap" between trapdoor permutations and claw-free permutations. Additionally, they can be viewed as the first security/efficiency separation between these basic cryptographic primitives. In other words, while it was already believed that certain cryptographic objects can be built from claw-free permutations but not from general trapdoor permutations, we show that certain important schemes (like FDH and PSS) provably work with either, but enjoy a much better tradeoff between security and efficiency when deployed with claw-free permutations.
TL;DR: A recursion for the number of permutations containing exactly one occurrence of a pattern of the first or the second of the aforementioned classes is presented, and an ordinary generating function is found for these numbers.
Proceedings Article•
9 Jul 2002TL;DR: A genetic algorithm (GA) is presented that uses a well-known greedy algorithm for structure learning (K2) and approximate inference by importance sampling as primitives in searching this permutation space and develops a flexible fitness measure based upon inferential loss given a specification of evidence.
Abstract: Greedy score-based algorithms for learning the structure of Bayesian networks may produce very different models depending on the order in which variables are scored, These models often vary significantly in quality when applied to inference, Unfortunately, finding the optimal ordering of inputs entails search through the permutation space of variables, Furthermore, in real-world applications of structure learning, the gold standard network is typically unknown, In this paper, we first present a genetic algorithm (GA) that uses a well-known greedy algorithm for structure learning (K2) and approximate inference by importance sampling as primitives in searching this permutation space, We then develop a flexible fitness measure based upon inferential loss given a specification of evidence, Finally, we evaluate this GA wrapper using the well-known networks Asia and ALARM and show that it is competitive with exhaustive enumeration in finding good orderings for K2, resulting in structures with low inferential loss under importance sampling.
TL;DR: The present paper proves the conjecture that the universal embedding of the U2n(2) dual polar space has dimension at least (4n+2)/3 and has conjectured equality by establishing a related result about permutation modules for GLn(4).
6 Jan 2002
TL;DR: In this paper, the authors study the problem of compressing massive tables within the partition-training paradigm introduced by Buchsbaum et al. [SODA'00], in which a table is partitioned by an off-line training procedure into disjoint intervals of columns, each of which is compressed separately by a standard, on-line compressor like gzip.
Abstract: We study the problem of compressing massive tables within the partition-training paradigm introduced by Buchsbaum et al. [SODA'00], in which a table is partitioned by an off-line training procedure into disjoint intervals of columns, each of which is compressed separately by a standard, on-line compressor like gzip. We provide a new theory that unifies previous experimental observations on partitioning and heuristic observations on column permutation, all of which are used to improve compression rates. Based on the theory, we devise the first on-line training algorithms for table compression, which can be applied to individual files, not just continuously operating sources; and also a new, off-line training algorithm, based on a link to the asymmetric traveling salesman problem, which improves on prior work by rearranging columns prior to partitioning. We demonstrate these results experimentally. On various test files, the on-line algorithms provide 35-55% improvement over gzip with negligible slowdown; the off-line reordering provides up to 20% further improvement over partitioning alone. We also show that a variation of the table compression problem is MAX-SNP hard.
TL;DR: This paper proves several contiguity results involving permutation pseudographs (contiguity is a kind of asymptotic equivalence of sequences of probability spaces) and shows that a random 4-regular pseudograph is contiguous with the sum of two permutations pseudographs.
Abstract: The space of permutation pseudographs is a probabilistic model of 2-regular pseudographs on n vertices, where a pseudograph is produced by choosing a permutation s of l1,2,…, nr uniformly at random and taking the n edges li,s(i)r. We prove several contiguity results involving permutation pseudographs (contiguity is a kind of asymptotic equivalence of sequences of probability spaces). Namely, we show that a random 4-regular pseudograph is contiguous with the sum of two permutation pseudographs, the sum of a permutation pseudograph and a random Hamilton cycle, and the sum of a permutation pseudograph and a random 2-regular pseudograph. (The sum of two random pseudograph spaces is defined by choosing a pseudograph from each space independently and taking the union of the edges of the two pseudographs.) All these results are proved simultaneously by working in a general setting, where each cycle of the permutation is given a nonnegative constant multiplicative weight. A further contiguity result is proved involving the union of a weighted permutation pseudograph and a random regular graph of arbitrary degree. All corresponding results for simple graphs are obtained as corollaries.
TL;DR: This work introduces a new method, called symmetry excluding search (SES), for excluding symmetries in constraint based search, which is the first declarative method that can be applied to arbitrary asymmetries, and proves correctness, completeness and symmetry exclusion properties.
Abstract: We introduce a new method, called i>symmetry excluding search (SES), for excluding symmetries in constraint based search. To our knowledge, it is the first declarative method that can be applied to i>arbitrary symmetries. The SES-method is based on the notion of symmetric constraints, which are used in our modification of a general constraint based search algorithm. The method does not influence the search strategy. Furthermore, it can be used with either the full set of symmetries, or a subset of all symmetries.
We proof correctness, completeness and symmetry exclusion properties of our method. Then, we show how to apply the SES-method in the special case of geometric symmetries (rotations and reflections) and permutation symmetries. Furthermore, we give results from practical applications.
TL;DR: In this article, the authors consider hypothesis testing using resampling or Monte Carlo methods, such as a bootstrap or a permutation procedure, and explore designs for resam sampling that minimize the expected number of resamples after meeting two constraints.
Abstract: This article considers hypothesis testing using resampling or Monte Carlo methods, such as a bootstrap or a permutation procedure, and explores designs for resampling that minimize the expected number of resamples after meeting two constraints. First, we bound the size of the test at the nominal level. Second, we bound the resampling risk, which we define as the expected value of the probability of reaching an accept/reject decision different from complete enumeration. This second bound holds over a postulated set of distributions for the p value, where each distribution is associated with a probability model of the data. In relation to these constraints, we examine the fixed resample size design and two sequential resampling designs, a simple curtailed sampling design, and a new, more complicated design with smaller expected resampling size.
1 Nov 2002
TL;DR: A modular proof of the strong normalisation of intuitionistic logic with permutation-conversions is presented, based on the notions of negative translation and CPS-simulation.
Abstract: We present a modular proof of the strong normalisation of intuitionistic logic with permutation-conversions. This proof is based on the notions of negative translation and CPS-simulation.