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Computer science problem
computer science, the longest increasing subsequence problem aims to find a subsequence of a given sequence in which the subsequence's elements are sorted
Longest increasing subsequence
Longest_increasing_subsequence
Sorting algorithm
variant of the algorithm efficiently computes the length of a longest increasing subsequence in a given array. The algorithm's name derives from a simplified
Patience_sorting
Mathematical binary relation
convergent subsequence whose limit is in X {\displaystyle X} . Subsequential limit Limit superior and limit inferior Longest increasing subsequence Longest alternating
Subsequence
Sufficiently long sequences of numbers have long monotonic subsequences
(r-1)(s-1)+1} contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s. The proof appeared in the
Erdős–Szekeres_theorem
Algorithmic problem on pairs of sequences
A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from
Longest_common_subsequence
Combinatorial problem
probability, and computer science, in the longest alternating subsequence problem, one wants to find a subsequence of a given sequence in which the elements
Longest alternating subsequence
Longest_alternating_subsequence
has applications to percolations and longest increasing subsequence. To study the longest increasing subsequence of a random permutation π {\displaystyle
Kingman's subadditive ergodic theorem
Kingman's_subadditive_ergodic_theorem
Mathematical formula for the number of Young tableaux
probability, and algorithm analysis; for example, the problem of longest increasing subsequences. A related formula gives the number of semi-standard Young
Hook_length_formula
Measure on group representations
combinatorial and probabilistic problems, especially in the study of longest increasing subsequence of a random permutation σ {\displaystyle \sigma } . As a result
Plancherel_measure
Natural number
permutations of six elements, exactly 238 of them have a unique longest increasing subsequence. There are 238 compact and paracompact hyperbolic groups of
238_(number)
makes a statement about the distribution of the length of the longest increasing subsequence in the limit. The theorem was influential in probability theory
Baik–Deift–Johansson_theorem
Topics referred to by the same term
server, provides location information Longest increasing subsequence, algorithm to find the longest increasing subsequence in an array of numbers Laser Isotope
LIS
Monoid of all words in the alphabet of positive integers modulo Knuth equivalence
operation given by Craige Schensted (1961) in his study of the longest increasing subsequence of a permutation. It was named the "monoïde plaxique" by Lascoux
Plactic_monoid
Probability distribution
system. It also appears in the distribution of the length of the longest increasing subsequence of random permutations, as large-scale statistics in the Kardar-Parisi-Zhang
Tracy–Widom_distribution
Russian mathematician (1933–2024)
representations of infinite symmetric groups and applications to the longest increasing subsequences. Vershik studied at Leningrad State University (later renamed
Anatoly_Vershik
Mathematician
Mathematics of Longest Increasing Subsequences - Book Review". ZbMath Open. Retrieved September 23, 2023. "The Surprising Mathematics of Longest Increasing Subsequences
Dan_Romik
become a superpattern. Arratia (1999) observes that, because the longest increasing subsequence of a random permutation has length (with high probability) approximately
Superpattern
Samplesort Longest common subsequence problem: Find the longest subsequence common to all sequences in a set of sequences Longest increasing subsequence problem:
List_of_algorithms
Bijective correspondence in mathematics
length of the longest increasing subsequence of σ1, ..., σn is equal to the length of the first row of P (and of Q). The length of the longest decreasing
Robinson–Schensted correspondence
Robinson–Schensted_correspondence
algorithm, also known as Hunt–McIlroy algorithm, is a solution to the longest common subsequence problem. It was one of the first non-heuristic algorithms used
Hunt–Szymanski_algorithm
Decomposition of an integer as a sum of positive integers
extended these results to determine the distribution of the longest increasing subsequence of a random permutation in terms of the Tracy–Widom distribution
Integer_partition
Mathematical problems related to differential equations
& Johansson (1999) on the distribution of the length of the longest increasing subsequence of a random permutation. Together with the study of B above
Riemann–Hilbert_problem
Diff and merge files on computers
[clarification needed] Some specialized file comparison tools find the longest increasing subsequence between two files. The rsync protocol uses a rolling hash function
File_comparison
Algorithm that arranges lists in order
it is extremely fast and demonstrates great asymptotic behavior as n increases. It also can be modified to provide stable behavior. Bucket sort is a
Sorting_algorithm
Class of algorithms operating on data streams
counting the number of inversions in a stream and finding the longest increasing subsequence.[citation needed] The performance of an algorithm that operates
Streaming_algorithm
Stochastic point process in mathematics
Young diagrams) plays an important role in the study of the longest increasing subsequence of a random permutation. The point process corresponding to
Determinantal_point_process
Property of a computational problem
problem has an optimal substructure. Longest common subsequence problem Longest increasing subsequence Longest palindromic substring All-Pairs Shortest
Optimal_substructure
Computer science problem
problem. The longest palindromic substring problem should not be confused with the different problem of finding the longest palindromic subsequence. This algorithm
Longest_palindromic_substring
Exponent of a power of two
in balanced binary search trees Exponentiation by squaring Longest increasing subsequence Binary logarithms also occur in the exponents of the time bounds
Binary_logarithm
Data mining technique
repeats, finding tandem repeats, and finding unique subsequences and missing (un-spelled) subsequences. Alignment problems: that deal with comparison between
Sequential_pattern_mining
Belgian-German professor of mathematics
Borel–Cantelli lemma BRS-inequality (Bruss-Robertson-Steele inequality) Longest increasing subsequence Pascal processes Last-arrival problem Bruss-Strategie Clinical
Franz_Thomas_Bruss
Partial differential equations of correlation functions
Kurt (June 1999), "On the distribution of the length of the longest increasing subsequence of random permutations" (PDF), J. Amer. Math. Soc., 12 (4):
Knizhnik–Zamolodchikov equations
Knizhnik–Zamolodchikov_equations
Characterizes the height of any finite partially ordered set
Gallai–Hasse–Roy–Vitaver theorem relating longest paths and colorings in graphs, and to the Erdős–Szekeres theorem on monotonic subsequences. The height of a partially
Mirsky's_theorem
Graph representing a permutation
time for permutation graphs by using a longest decreasing subsequence algorithm. likewise, an increasing subsequence in a permutation corresponds to an independent
Permutation_graph
Alejandro; Rao, S.Srinivasa; Safari, Mohammad Ali (August 2004). "Longest increasing subsequences in sliding windows". Theoretical Computer Science. 321 (2–3):
List of University of Waterloo people
List_of_University_of_Waterloo_people
trees (to get MUMs), the second part in the longest increasing subsequence or longest common subsequences (to order MUMs), lastly any alignment to close
MUMmer
Swedish mathematician
Johansson, Kurt (1999). "On the distribution of the length of the longest increasing subsequence of random permutations". Journal of the American Mathematical
Kurt Johansson (mathematician)
Kurt_Johansson_(mathematician)
Searching for patterns in compressed data
algorithms that provide running time that grows logarithmically with the increase of string and pattern length. Joel Grus (2019). Data Science from Scratch
Compressed_pattern_matching
Property of some mathematical functions
. , k {\displaystyle 1,2,...,k} . The expected length of the longest common subsequence is a super-additive function of n {\displaystyle n} , and thus
Subadditivity
Task of computing complete subgraphs
longest decreasing subsequence of the permutation defining the graph and can be found using known algorithms for the longest decreasing subsequence problem
Clique_problem
Well-quasi-ordering of finite trees
of letters x i , … , x 2 i {\displaystyle x_{i},\ldots ,x_{2i}} is a subsequence of any later block x j , … , x 2 j {\displaystyle x_{j},\ldots ,x_{2j}}
Kruskal's_tree_theorem
Deterministic finite automaton accepting set of all suffixes of particular string
Finding the longest substring of S {\displaystyle S} occurring at least twice in O ( | S | ) {\displaystyle O(|S|)} , Finding the longest common substring
Suffix_automaton
Directed graph with no directed cycles
given sequences. When many of the sequences share the same subsequences, these shared subsequences can be represented by a shared part of the DAG, allowing
Directed_acyclic_graph
Type of permutation
{\displaystyle S(r,k)} denotes Stirling numbers of the second kind. Longest alternating subsequence Boustrophedon transform Fence (mathematics), a partially ordered
Alternating_permutation
American mathematician
world", Maine Times, pp. 20–21 Schensted, C. (1961), "Longest increasing and decreasing subsequences", Canadian Journal of Mathematics, 13: 179–191, doi:10
Craige_Schensted
Self-balancing binary search tree data structure
Since the length of the subsequences in S is ∈ O ( | I | ) {\displaystyle \in O(|I|)} and in every stage the subsequences are being cut in half, the
Red–black_tree
Examination of the frequency, patterns, and graphs of citations in documents
to compute citation pattern similarities. Citation patterns represent subsequences non-exclusively containing citations shared by the documents compared
Citation_analysis
Algorithm for evaluating the quality of machine-translated text
(2004) "Automatic Evaluation of Machine Translation Quality Using Longest Common Subsequence and Skip-Bigram Statistics Archived 2008-07-05 at the Wayback
BLEU
Wireless positioning technology
other subsequences: The first one is called synchronization sequence (abbreviated to SYNC) and it is the longest one. Its purpose is to increase the effective
UWB_ranging
Process in bioinformatics that identifies equivalent sites within molecular sequences
given pairwise alignment is the 'maximal unique match' (MUM), or the longest subsequence that occurs in both query sequences. Longer MUM sequences typically
Sequence_alignment
Process of detecting plagiarism and/or copyright infringement
to compute citation pattern similarities. Citation patterns represent subsequences non-exclusively containing citations shared by the documents compared
Content_similarity_detection
Application of computer science in biology
number of bioinformatics applications, such as computing the longest common subsequence of two genes or comparing variants of certain diseases.[citation
Computational_biology
Mathematical rule
JSTOR 2371609 Zbl0019.25102 Schensted, C. (1961), "Longest increasing and decreasing subsequences", Canadian Journal of Mathematics, 13: 179–191, doi:10
Littlewood–Richardson_rule
Analysis of sets of categorical sequences
(derived from length of longest common subsequence), LCP (from length of longest common prefix), NMS (number of matching subsequences), and NMSMST and SVRspell
Sequence analysis in social sciences
Sequence_analysis_in_social_sciences
Greek astronomer, geographer and mathematician (c. 190 – c. 120 BCE)
of ways of adding one or more pairs of parentheses around consecutive subsequences of two or more items in any sequence of ten symbols. This has led to
Hipparchus
Methods in computational biology
which gives final ACS measure between the two strings (A and B). The subsequence/substring search can be efficiently performed by using suffix trees.
Alignment-free sequence analysis
Alignment-free_sequence_analysis
Method for discovering interesting relations between variables in databases
age into 5-year-increment ranged Sequential pattern mining discovers subsequences that are common to more than minsup (minimum support threshold) sequences
Association_rule_learning
Software for understanding biological data
4 k {\displaystyle 4^{k}} whose entries count the appearance of each subsequence of length k {\displaystyle k} in a given sequence. Since for a value
Machine learning in bioinformatics
Machine_learning_in_bioinformatics
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