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A class of orders with linear? time sorting algorithm [article]

Laurent Lyaudet
2018 arXiv   pre-print
The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine.  ...  In this article, we give a precise mathematical meaning to 'linear? time' that matches experimental behaviour of the algorithm.  ...  We thank Pascal Koiran and Gilles Villard for useful corrections on the complexity of results about rationals.  ... 
arXiv:1809.00954v5 fatcat:wtwbwg5agza4fgvmyz3w3ar5ka

A study on design of object sorting algorithms in the industrial application using hyperspectral imaging

Pavel Paclík, Raimund Leitner, Robert P. W. Duin
2006 Journal of Real-Time Image Processing  
The paper provides a case-study on algorithm design in a real-world industrial sorting problem. Four groups of algorithms are studied varying the level of prior knowledge about the sorting problem.  ...  Design of object sorting algorithms is a challenging pattern recognition problem due to its multi-level nature.  ...  This research is/was supported by the Technology Foundation STW, applied science division of NWO and the technology program of the Ministry of Economic Affairs.  ... 
doi:10.1007/s11554-006-0018-5 fatcat:q7depdun4reulixglcpppcug6y

A Polynomial Algorithm for a Class of 0–1 Fractional Programming Problems Involving Composite Functions, with an Application to Additive Clustering [chapter]

Pierre Hansen, Christophe Meyer
2014 Clusters, Orders, and Trees: Methods and Applications  
linear functionˆ. / D max In particular we show that when ' is convex and increasing, is concave, increasing and strictly positive, v and w are supermodular and either v or w has a monotonicity property  ...  We apply this result to show that a 0-1 fractional programming problem arising in additive clustering can be solved in polynomial time.  ...  [22] have developed an algorithm that solves a special class of parametric minimum cut problem with a single parameter in the same complexity time than what would be necessary to solve the minimum cut  ... 
doi:10.1007/978-1-4939-0742-7_2 fatcat:ldyrcdthpfhldj4wtlvge3o7sm

A dedicated hardware system for a class of nonlinear order statistics rational hybrid filters with applications to image processing

L. Khriji, G. Bernacchia, M. Gabbouj, G. Sicuranza
1999 Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348)  
A dedicated hardware system is developed for a recent class of nonlinear hybrid filters called Order Statistics-Rational Hybrid Filters (OSRHF).  ...  The proposed hardware system uses a residue number system (RNS) to compute the numerator and the denominator of the rational filter.  ...  In any case the presence of the square function implies that a scaling algorithm is necessary in order to calculate numerator and denominator.  ... 
doi:10.1109/icip.1999.822930 dblp:conf/icip/KhrijiBGS99 fatcat:jkvf7ubxx5cbbfao7slg7nn3tm

On the asymptotic solutions of a class of ordinary differential equations of the fourth order, with special reference to an equation of hydrodynamics

Rudolph E. Langer
1957 Transactions of the American Mathematical Society  
Since the functions G&(z) and G6(z) vanish, and are therefore analytic, the differential equation (20.1) is seen to comply with the requirements for inclusion in the category 1, at least ior all m that  ...  An irregular differential equation (1.1) shall be classed as in the category 3, with respect to a given integer m, if the assertions (17.2) apply to it for some pair of integers a and v, with a <v ^m.  ...  In every instance of this sort, the associated equation L(u)=0, for m= =0, is formally solvable by a power series in 1/X with coefficients that are analytic in z.  ... 
doi:10.1090/s0002-9947-1957-0083637-0 fatcat:uykaz7i2mvdubpv2dcaoixnfrm

On the Asymptotic Solutions of a Class of Ordinary Differential Equations of the Fourth Order, with Special Reference to an Equation of Hydrodynamics

Rudolph E. Langer
1957 Transactions of the American Mathematical Society  
Since the functions G&(z) and G6(z) vanish, and are therefore analytic, the differential equation (20.1) is seen to comply with the requirements for inclusion in the category 1, at least ior all m that  ...  An irregular differential equation (1.1) shall be classed as in the category 3, with respect to a given integer m, if the assertions (17.2) apply to it for some pair of integers a and v, with a <v ^m.  ...  In every instance of this sort, the associated equation L(u)=0, for m= =0, is formally solvable by a power series in 1/X with coefficients that are analytic in z.  ... 
doi:10.2307/1992896 fatcat:2bbuzwxpkfgt3iklechlpjfray

Sorting in Linear Time?

Arne Andersson, Torben Hagerup, Stefan Nilsson, Rajeev Raman
1998 Journal of computer and system sciences (Print)  
Provided that w 2 (log n)z+', for some fixed e > 0, the sorting can even be accomplished in linear expected time with a randomized algorithm.  ...  Both of our algorithms parallelize without loss on a unitcost PRAM with a word length of w bits.  ...  This leaves us with the problem of sorting n integers of at most [zo/ (log n)21 bits each, which can be done in O(n) time using the algorithm of Albers and Hagerup. 3 Sorting in linear expected time  ... 
doi:10.1006/jcss.1998.1580 fatcat:czaka6rbejgdtgzcunuyfix42i

Sorting in linear time?

Arne Andersson, Torben Hagerup, Stefan Nilsson, Rajeev Raman
1995 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95  
Provided that w 2 (log n)z+', for some fixed e > 0, the sorting can even be accomplished in linear expected time with a randomized algorithm.  ...  Both of our algorithms parallelize without loss on a unitcost PRAM with a word length of w bits.  ...  This leaves us with the problem of sorting n integers of at most [zo/ (log n)21 bits each, which can be done in O(n) time using the algorithm of Albers and Hagerup. 3 Sorting in linear expected time  ... 
doi:10.1145/225058.225173 dblp:conf/stoc/AnderssonHNR95 fatcat:5pl4yf3zi5fq7j5omkeki7kmbi

Training linear SVMs in linear time

Thorsten Joachims
2006 Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '06  
This paper presents a Cutting-Plane Algorithm for training linear SVMs that provably has training time O(sn) for classification problems and O(sn log(n)) for ordinal regression problems.  ...  Empirically, the Cutting-Plane Algorithm is several orders of magnitude faster than decomposition methods like SVM-Light for large datasets.  ...  By going through the examples in order of w T xi, the algorithm can keep track of a = |l : (y Lemma 3 . 3 Each iteration of Algorithm 2 requires time O(sn + n log(n) + Rn) for a constant working set  ... 
doi:10.1145/1150402.1150429 dblp:conf/kdd/Joachims06 fatcat:bdns3nypxbd4fmdmyi2c57kysu

Fast algorithms for linear prediction and system identification filters with linear phase

S. Marple
1982 IEEE Transactions on Acoustics Speech and Signal Processing  
A class of selection algorithms by binary partition is very efficient for median and rank order filtering. A unified discussion of . IEEE Log Number 9210117 these algorithms is presented.  ...  Binary partition algorithms have better time-area complexity than sorting methods. Counting, firing, and updating are three basic steps. A generic structure is proposed to realize these algorithms.  ...  The first one is to implement order statistic filtering by systolic algorithms with a linear array of identical processing elements [15] .  ... 
doi:10.1109/tassp.1982.1163987 fatcat:amvihsxvi5bxnf7x6rs2fi4uxe

On Multiple Linear Approximations [chapter]

Alex Biryukov, Christophe De Cannière, Michaël Quisquater
2004 Lecture Notes in Computer Science  
In order to substantiate the theoretical claims, we benchmarked the attacks against reduced-round versions of DES and observed a clear reduction of the data and time complexities, in almost perfect correspondence  ...  The complexities are reduced by several orders of magnitude for Algorithm 1, and the significant improvement in the case of Algorithm 2 suggests that this approach may outperform the currently best attacks  ...  values to construct a sorted list, starting with the class with the smallest distance.  ... 
doi:10.1007/978-3-540-28628-8_1 fatcat:xgv2gm44azawphdmjs7eydbgjm

Linear complexity assertions for sorting

N.R. Saxena, E.J. McCluskey
1994 IEEE Transactions on Software Engineering  
Permutation and order assertions are sufficient for the detection of errors in the execution of sorting programs; however, in terms of execution time these assertions cost the same as sorting programs.  ...  The order assertion checks if the sorted data is in ascending or descending order. The permutation assertion checks if the output data produced by sorting is a permutation of the original input data.  ...  ACKNOWLEDGMENT We would like to thank all of the referees for very valuable suggestions.  ... 
doi:10.1109/32.295891 fatcat:tyxkpkk5jzgltnzu3mdl6np25q

Linear work suffix array construction

Juha Kärkkäinen, Peter Sanders, Stefan Burkhardt
2006 Journal of the ACM  
We narrow this gap between theory and practice with a simple linear-time construction algorithm for suffix arrays.  ...  This view leads to a generalized algorithm, DC, that allows a space-efficient implementation and, moreover, supports the choice of a space-time tradeoff.  ...  Linear-time algorithm We begin with a detailed description of the simple linear-time algorithm, which we call DC3 (for Difference Cover modulo 3, see Section 4).  ... 
doi:10.1145/1217856.1217858 fatcat:icwh6toiwvfqbm3xot6obq4rqa

Binar Sort: A Linear Generalized Sorting Algorithm [article]

William F. Gilreath
2011 arXiv   pre-print
Linear O(N) sorting algorithms exist, but use a priori knowledge of the data to use a specific property of the data and thus have greater performance.  ...  A general-purpose, linear sorting algorithm in the context of the trade-off of performance for generality at first consideration seems implausible.  ...  The practical performance time is what is expected, linear time with a constant factor. ments are in sorted order, and return a logical true or false.  ... 
arXiv:0811.3448v2 fatcat:l5ggl6gzxjhdnmex6mfmhmf2ny

Linear discriminant initialization for feed-forward neural networks [article]

Marissa Masden, Dev Sinha
2020 arXiv   pre-print
Informed by the basic geometry underlying feed forward neural networks, we initialize the weights of the first layer of a neural network using the linear discriminants which best distinguish individual  ...  classes.  ...  Instead, we may perform the linear discriminant analysis on a subset of input variables at a time.  ... 
arXiv:2007.12782v2 fatcat:pdgxtzlhfzgzfeyyzfbzor2lni
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