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Journal articles on the topic 'Longest increasing subsequences'

Author: Grafiati

Published: 23 September 2022

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1

Russo, Luıs, and Alexandre Francisco. "Small Longest Tandem Scattered Subsequences." Scientific Annals of Computer Science 31, no. 1 (August 9, 2021): 79–110. http://dx.doi.org/10.7561/sacs.2021.1.79.

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We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm, therefore its performance improves if the string is not self similar, which occurs naturally on strings over large alphabets. Our algorithm relies on new results for data structures that support dynamic longest increasing sub-sequences. In the process we also obtain improved algorithms for the decremental string comparison problem.

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2

Albert, Michael H., Alexander Golynski, Angèle M. Hamel, Alejandro López-Ortiz, S. Srinivasa Rao, and Mohammad Ali Safari. "Longest increasing subsequences in sliding windows." Theoretical Computer Science 321, no. 2-3 (August 2004): 405–14. http://dx.doi.org/10.1016/j.tcs.2004.03.057.

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3

Bóna, Miklós, Marie-Louise Lackner, and Bruce E. Sagan. "Longest Increasing Subsequences and Log Concavity." Annals of Combinatorics 21, no. 4 (August 19, 2017): 535–49. http://dx.doi.org/10.1007/s00026-017-0365-x.

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4

Groeneboom, Piet. "Hydrodynamical methods for analyzing longest increasing subsequences." Journal of Computational and Applied Mathematics 142, no. 1 (May 2002): 83–105. http://dx.doi.org/10.1016/s0377-0427(01)00461-7.

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5

Bespamyatnikh, Sergei, and Michael Segal. "Enumerating longest increasing subsequences and patience sorting." Information Processing Letters 76, no. 1-2 (November 2000): 7–11. http://dx.doi.org/10.1016/s0020-0190(00)00124-1.

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6

He, Xiaozhou, and Yinfeng Xu. "The longest commonly positioned increasing subsequences problem." Journal of Combinatorial Optimization 35, no. 2 (September 9, 2017): 331–40. http://dx.doi.org/10.1007/s10878-017-0170-9.

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7

DEUSCHEL, JEAN-DOMINIQUE, and OFER ZEITOUNI. "On Increasing Subsequences of I.I.D. Samples." Combinatorics, Probability and Computing 8, no. 3 (May 1999): 247–63. http://dx.doi.org/10.1017/s0963548399003776.

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We study the fluctuations, in the large deviations regime, of the longest increasing sub-sequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation.

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8

Li, Youhuan, Lei Zou, Huaming Zhang, and Dongyan Zhao. "Computing longest increasing subsequences over sequential data streams." Proceedings of the VLDB Endowment 10, no. 3 (November 2016): 181–92. http://dx.doi.org/10.14778/3021924.3021934.

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9

Aldous, D., and P. Diaconis. "Hammersley's interacting particle process and longest increasing subsequences." Probability Theory and Related Fields 103, no. 2 (June 1995): 199–213. http://dx.doi.org/10.1007/bf01204214.

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10

Kutz, Martin, Gerth Stølting Brodal, Kanela Kaligosi, and Irit Katriel. "Faster algorithms for computing longest common increasing subsequences." Journal of Discrete Algorithms 9, no. 4 (December 2011): 314–25. http://dx.doi.org/10.1016/j.jda.2011.03.013.

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11

ANGEL, OMER, RICHÁRD BALKA, and YUVAL PERES. "Increasing subsequences of random walks." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 1 (September 23, 2016): 173–85. http://dx.doi.org/10.1017/s0305004116000797.

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AbstractGiven a sequence of n real numbers {Si}i⩽n, we consider the longest weakly increasing subsequence, namely i1 < i2 < . . . < iL with Sik ⩽ Sik+1 and L maximal. When the elements Si are i.i.d. uniform random variables, Vershik and Kerov, and Logan and Shepp proved that ${\mathbb E} L=(2+o(1)) \sqrt{n}$.We consider the case when {Si}i⩽n is a random walk on ℝ with increments of mean zero and finite (positive) variance. In this case, it is well known (e.g., using record times) that the length of the longest increasing subsequence satisfies ${\mathbb E} L\geq c\sqrt{n}$. Our main result is an upper bound ${\mathbb E} L\leq n^{1/2 + o(1)}$, establishing the leading asymptotic behavior. If {Si}i⩽n is a simple random walk on ℤ, we improve the lower bound by showing that ${\mathbb E} L \geq c\sqrt{n} \log{n}$.We also show that if {Si} is a simple random walk in ℤ2, then there is a subsequence of {Si}i⩽n of expected length at least cn1/3 that is increasing in each coordinate. The above one-dimensional result yields an upper bound of n1/2+o(1). The problem of determining the correct exponent remains open.

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12

KIWI, MARCOS, and JOSÉ A. SOTO. "Longest Increasing Subsequences of Randomly Chosen Multi-Row Arrays." Combinatorics, Probability and Computing 24, no. 1 (October 2, 2014): 254–93. http://dx.doi.org/10.1017/s0963548314000637.

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A two-row array of integers \[ \alpha_{n}= \begin{pmatrix}a_1 & a_2 & \cdots & a_n\\ b_1 & b_2 & \cdots & b_n \end{pmatrix} \] is said to be in lexicographic order if its columns are in lexicographic order (where character significance decreases from top to bottom, i.e., either ak < ak+1, or bk ≤ bk+1 when ak = ak+1). A length ℓ (strictly) increasing subsequence of αn is a set of indices i1 < i2 < ⋅⋅⋅ < iℓ such that ai1 < ai2 < ⋅⋅⋅ < aiℓ and bi1 < bi2 < ⋅⋅⋅ < biℓ. We are interested in the statistics of the length of a longest increasing subsequence of αn chosen according to ${\cal D}$n, for different families of distributions ${\cal D} = ({\cal D}_{n})_{n\in\NN}$, and when n goes to infinity. This general framework encompasses well-studied problems such as the so-called longest increasing subsequence problem, the longest common subsequence problem, and problems concerning directed bond percolation models, among others. We define several natural families of different distributions and characterize the asymptotic behaviour of the length of a longest increasing subsequence chosen according to them. In particular, we consider generalizations to d-row arrays as well as symmetry-restricted two-row arrays.

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13

Löwe, Matthias, and Franz Merkl. "Moderate deviations for longest increasing subsequences: The upper tail." Communications on Pure and Applied Mathematics 54, no. 12 (October 1, 2001): 1488–519. http://dx.doi.org/10.1002/cpa.10010.

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14

Su, Zhong-gen. "LIL for the Length of the Longest Increasing Subsequences." Acta Mathematicae Applicatae Sinica, English Series 36, no. 2 (March 2020): 283–93. http://dx.doi.org/10.1007/s10255-020-0942-3.

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15

Liben-Nowell, David, Erik Vee, and An Zhu. "Finding longest increasing and common subsequences in streaming data." Journal of Combinatorial Optimization 11, no. 2 (March 2006): 155–75. http://dx.doi.org/10.1007/s10878-006-7125-x.

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16

Chen, Erdong, Linji Yang, and Hao Yuan. "Longest increasing subsequences in windows based on canonical antichain partition." Theoretical Computer Science 378, no. 3 (June 2007): 223–36. http://dx.doi.org/10.1016/j.tcs.2007.02.032.

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17

MANSOUR, Toufik, and Gökhan YILDIRIM. "Longest increasing subsequences in involutions avoiding patterns of length three." TURKISH JOURNAL OF MATHEMATICS 43, no. 5 (September 28, 2019): 2183–92. http://dx.doi.org/10.3906/mat-1901-86.

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18

Gao, Alice L. L., Matthew H. Y. Xie, and Arthur L. B. Yang. "Schur positivity and log-concavity related to longest increasing subsequences." Discrete Mathematics 342, no. 9 (September 2019): 2570–78. http://dx.doi.org/10.1016/j.disc.2019.05.027.

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19

Thomas, Hugh, and Alexander Yong. "Longest increasing subsequences, Plancherel-type measure and the Hecke insertion algorithm." Advances in Applied Mathematics 46, no. 1-4 (January 2011): 610–42. http://dx.doi.org/10.1016/j.aam.2009.07.005.

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20

Laaksonen, Antti, and Kjell Lemström. "Discovering distorted repeating patterns in polyphonic music through longest increasing subsequences." Journal of Mathematics and Music 15, no. 2 (April 5, 2021): 99–111. http://dx.doi.org/10.1080/17459737.2021.1896811.

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21

Aldous, David, and Persi Diaconis. "Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem." Bulletin of the American Mathematical Society 36, no. 04 (July 21, 1999): 413–33. http://dx.doi.org/10.1090/s0273-0979-99-00796-x.

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22

Mansour, Toufik, and Gökhan Yıldırım. "Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences." Advances in Applied Mathematics 116 (May 2020): 102002. http://dx.doi.org/10.1016/j.aam.2020.102002.

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23

García, Jesús E., and Verónica A. González-López. "Random Permutations, Non-Decreasing Subsequences and Statistical Independence." Symmetry 12, no. 9 (August 26, 2020): 1415. http://dx.doi.org/10.3390/sym12091415.

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In this paper, we show how the longest non-decreasing subsequence, identified in the graph of the paired marginal ranks of the observations, allows the construction of a statistic for the development of an independence test in bivariate vectors. The test works in the case of discrete and continuous data. Since the present procedure does not require the continuity of the variables, it expands the proposal introduced in Independence tests for continuous random variables based on the longest increasing subsequence (2014). We show the efficiency of the procedure in detecting dependence in real cases and through simulations.

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24

Mendonça, J. Ricardo G. "Empirical scaling of the length of the longest increasing subsequences of random walks." Journal of Physics A: Mathematical and Theoretical 50, no. 8 (January 18, 2017): 08LT02. http://dx.doi.org/10.1088/1751-8121/aa56a3.

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25

Wang, Qingguo, Mian Pan, Yi Shang, and Dmitry Korkin. "A Fast Heuristic Search Algorithm for Finding the Longest Common Subsequence of Multiple Strings." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 4, 2010): 1287–92. http://dx.doi.org/10.1609/aaai.v24i1.7493.

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Finding the longest common subsequence (LCS) of multiple strings is an NP-hard problem, with many applications in the areas of bioinformatics and computational genomics. Although significant efforts have been made to address the problem and its special cases, the increasing complexity and size of biological data require more efficient methods applicable to an arbitrary number of strings. In this paper, a novel search algorithm, MLCS-A*, is presented for the general case of multiple LCS (or MLCS) problems. MLCS-A* is a variant of the A* algorithm. It maximizes a new heuristic estimate of the LCS in each search step so that the longest common subsequence can be found. As a natural extension of MLCS-A*, a fast algorithm, MLCS-APP, is also proposed to deal with large volume of biological data for which finding a LCS within reasonable time is impossible. The benchmark test shows that MLCS-APP is able to extract common subsequences close to the optimal ones and that MLCS-APP significantly outperforms existing heuristic approaches. When applied to 8 protein domain families, MLCS-APP produced more accurate results than existing multiple sequence alignment methods.

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26

Li, Yanni, Yuping Wang, and Liang Bao. "FACC: A Novel Finite Automaton Based on Cloud Computing for the Multiple Longest Common Subsequences Search." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/310328.

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Searching for the multiple longest common subsequences (MLCS) has significant applications in the areas of bioinformatics, information processing, and data mining, and so forth, Although a few parallel MLCS algorithms have been proposed, the efficiency and effectiveness of the algorithms are not satisfactory with the increasing complexity and size of biologic data. To overcome the shortcomings of the existing MLCS algorithms, and considering that MapReduce parallel framework of cloud computing being a promising technology for cost-effective high performance parallel computing, a novel finite automaton (FA) based on cloud computing called FACC is proposed under MapReduce parallel framework, so as to exploit a more efficient and effective general parallel MLCS algorithm. FACC adopts the ideas of matched pairs and finite automaton by preprocessing sequences, constructing successor tables, and common subsequences finite automaton to search for MLCS. Simulation experiments on a set of benchmarks from both real DNA and amino acid sequences have been conducted and the results show that the proposed FACC algorithm outperforms the current leading parallel MLCS algorithm FAST-MLCS.

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27

Breton, Jean-Christophe, and Christian Houdré. "On the limiting law of the length of the longest common and increasing subsequences in random words." Stochastic Processes and their Applications 127, no. 5 (May 2017): 1676–720. http://dx.doi.org/10.1016/j.spa.2016.09.005.

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28

Mendonça, J. Ricardo G. "A numerical investigation into the scaling behavior of the longest increasing subsequences of the symmetric ultra-fat tailed random walk." Physics Letters A 384, no. 29 (October 2020): 126753. http://dx.doi.org/10.1016/j.physleta.2020.126753.

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29

Corwin, Ivan. "Commentary on “Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem” by David Aldous and Persi Diaconis." Bulletin of the American Mathematical Society 55, no. 3 (April 18, 2018): 363–74. http://dx.doi.org/10.1090/bull/1623.

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30

Adler, Mark, Pierre van Moerbeke, and Pol Vanhaecke. "Singularity confinement for a class of m -th order difference equations of combinatorics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1867 (July 17, 2007): 877–922. http://dx.doi.org/10.1098/rsta.2007.2090.

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In a recent publication, it was shown that a large class of integrals over the unitary group U ( n ) satisfy nonlinear, non-autonomous difference equations over n , involving a finite number of steps; special cases are generating functions appearing in questions of the longest increasing subsequences in random permutations and words. The main result of the paper states that these difference equations have the discrete Painlevé property ; roughly speaking, this means that after a finite number of steps the solution to these difference equations may develop a pole (Laurent solution), depending on the maximal number of free parameters, and immediately after be finite again (‘ singularity confinement ’). The technique used in the proof is based on an intimate relationship between the difference equations (discrete time) and the Toeplitz lattice (continuous time differential equations); the point is that the Painlevé property for the discrete relations is inherited from the Painlevé property of the (continuous) Toeplitz lattice.

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31

Elmasry, Amr. "The longest almost-increasing subsequence." Information Processing Letters 110, no. 16 (July 2010): 655–58. http://dx.doi.org/10.1016/j.ipl.2010.05.022.

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32

Kiyomi, Masashi, Hirotaka Ono, Yota Otachi, Pascal Schweitzer, and Jun Tarui. "Space-Efficient Algorithms for Longest Increasing Subsequence." Theory of Computing Systems 64, no. 3 (January 22, 2019): 522–41. http://dx.doi.org/10.1007/s00224-018-09908-6.

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33

Geissmann, Barbara. "Longest Increasing Subsequence under Persistent Comparison Errors." Theory of Computing Systems 64, no. 4 (February 20, 2020): 662–80. http://dx.doi.org/10.1007/s00224-020-09966-9.

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34

Li, Youhuan, Lei Zou, Huaming Zhang, and Dongyan Zhao. "Longest Increasing Subsequence Computation over Streaming Sequences." IEEE Transactions on Knowledge and Data Engineering 30, no. 6 (June 1, 2018): 1036–49. http://dx.doi.org/10.1109/tkde.2017.2761345.

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35

Houdré, Christian, Jüri Lember, and Heinrich Matzinger. "On the longest common increasing binary subsequence." Comptes Rendus Mathematique 343, no. 9 (November 2006): 589–94. http://dx.doi.org/10.1016/j.crma.2006.10.004.

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36

Itskovich, Elizabeth J., and Vadim E. Levit. "What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?" Algorithms 12, no. 11 (November 7, 2019): 237. http://dx.doi.org/10.3390/a12110237.

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As a kind of converse of the celebrated Erdős–Szekeres theorem, we present a necessary and sufficient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths x and y, respectively.

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37

Yao, Linyi, Qiao Dong, Jiwang Jiang, and Fujian Ni. "Establishment of Prediction Models of Asphalt Pavement Performance based on a Novel Data Calibration Method and Neural Network." Transportation Research Record: Journal of the Transportation Research Board 2673, no. 1 (January 2019): 66–82. http://dx.doi.org/10.1177/0361198118822501.

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This paper aims to develop models to forecast the deterioration of pavement conditions including rutting, roughness, skid-resistance, transverse cracking, and pavement surface distress. A data quality control method was proposed to rebuild the performance data based on the idea of longest increasing or decreasing subsequences. Neural network (NN) was used to develop the five models, and principal component analysis (PCA) was applied to reduce the dimension of traffic variables. The influence of different input variables on the model outputs was discussed respectively by comparing their mean impact values (MIV). Results show that the proposed NN models demonstrated great potential for accurate prediction of pavement conditions, with an average testing R-square of 0.8692. The results of sensitivity analysis revealed that recent pavement conditions may influence the future pavement conditions significantly. Rutting and roughness were sensitive to pavement age and maintenance type. The materials of original pavement asphalt layer were highly relevant to the prediction of pavement roughness, skid-resistance, and pavement surface distress. Moreover, traffic loads obviously affected the pavement skid-resistance and transverse cracking. Pavement and bridge had different effect on surface distress. The material of the base has a remarkable impact on the initiation and development of transverse cracks. Disease treatment in terms of pavement cracking—such as sticking the cracks, excavating and filling the cracks—shows a high MIV in the prediction model of transverse cracking and pavement surface distress.

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38

Crochemore, Maxime, and Ely Porat. "Fast computation of a longest increasing subsequence and application." Information and Computation 208, no. 9 (September 2010): 1054–59. http://dx.doi.org/10.1016/j.ic.2010.04.003.

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39

Duraj, Lech, Marvin Künnemann, and Adam Polak. "Tight Conditional Lower Bounds for Longest Common Increasing Subsequence." Algorithmica 81, no. 10 (July 23, 2018): 3968–92. http://dx.doi.org/10.1007/s00453-018-0485-7.

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40

Chan, Wun-Tat, Yong Zhang, Stanley P. Y. Fung, Deshi Ye, and Hong Zhu. "Efficient algorithms for finding a longest common increasing subsequence." Journal of Combinatorial Optimization 13, no. 3 (December 29, 2006): 277–88. http://dx.doi.org/10.1007/s10878-006-9031-7.

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41

Albert, M. H., M. D. Atkinson, Doron Nussbaum, Jörg-Rüdiger Sack, and Nicola Santoro. "On the longest increasing subsequence of a circular list." Information Processing Letters 101, no. 2 (January 2007): 55–59. http://dx.doi.org/10.1016/j.ipl.2006.08.003.

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42

Pemantle, Robin, and Yuval Peres. "Non-universality for longest increasing subsequence of a random walk." Latin American Journal of Probability and Mathematical Statistics 14, no. 1 (2017): 327. http://dx.doi.org/10.30757/alea.v14-18.

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43

Yang, I.-Hsuan, Chien-Pin Huang, and Kun-Mao Chao. "A fast algorithm for computing a longest common increasing subsequence." Information Processing Letters 93, no. 5 (March 2005): 249–53. http://dx.doi.org/10.1016/j.ipl.2004.10.014.

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44

Deorowicz, Sebastian. "An algorithm for solving the longest increasing circular subsequence problem." Information Processing Letters 109, no. 12 (May 2009): 630–34. http://dx.doi.org/10.1016/j.ipl.2009.02.019.

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45

Lo, Shou-Fu, Kuo-Tsung Tseng, Chang-Biau Yang, and Kuo-Si Huang. "A diagonal-based algorithm for the longest common increasing subsequence problem." Theoretical Computer Science 815 (May 2020): 69–78. http://dx.doi.org/10.1016/j.tcs.2020.02.024.

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46

Ramanan, Prakash. "Tight Ω(nlgn) lower bound for finding a longest increasing subsequence." International Journal of Computer Mathematics 65, no. 3-4 (January 1997): 161–64. http://dx.doi.org/10.1080/00207169708804607.

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47

Sakai, Yoshifumi. "A linear space algorithm for computing a longest common increasing subsequence." Information Processing Letters 99, no. 5 (September 2006): 203–7. http://dx.doi.org/10.1016/j.ipl.2006.05.005.

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48

Duraj, Lech. "A linear algorithm for 3-letter longest common weakly increasing subsequence." Information Processing Letters 113, no. 3 (February 2013): 94–99. http://dx.doi.org/10.1016/j.ipl.2012.11.007.

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49

García, Jesús E., and V. A. González-López. "Independence tests for continuous random variables based on the longest increasing subsequence." Journal of Multivariate Analysis 127 (May 2014): 126–46. http://dx.doi.org/10.1016/j.jmva.2014.02.010.

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50

Houdré, Christian, and Zsolt Talata. "On the rate of approximation in finite-alphabet longest increasing subsequence problems." Annals of Applied Probability 22, no. 6 (December 2012): 2539–59. http://dx.doi.org/10.1214/12-aap853.

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