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Counting Distinct Strings

D. Moore, W. F. Smyth, D. Miller
1999 Algorithmica  
This paper discusses how to count and generate strings that are \distinct" in two senses: p-distinct and b-distinct.  ...  W e p r e s e n t algorithms to compute, in constant time per string, all p-distinct (respectively, b-distinct) strings of length n formed using exactly k letters, and we a l s o s h o w h o w to compute  ...  DISTINCT BORDER ARRAYS In this section we consider how to generate and how to count b-distinct strings.  ... 
doi:10.1007/pl00009247 fatcat:d4ywnnm4hbarjmlsfgyebclvpa

Counting suffix arrays and strings

Klaus-Bernd Schürmann, Jens Stoye
2008 Theoretical Computer Science  
For each such equivalence class, we count the number of strings contained in it. We also give exact formulas for computing the number of equivalence classes.  ...  For a fixed alphabet size and string length, we divide the set of all strings into equivalence classes of strings that share the same suffix array.  ...  Theorem 4 gave the number of string-distinct strings and to count the order-distinct strings we just sum up over all possible κ.  ... 
doi:10.1016/j.tcs.2008.01.011 fatcat:tqb7fk5inrgpfjdhd6uibqkfb4

The Number of Distinct Subsequences of a Random Binary String [article]

Michael J. Collins
2013 arXiv   pre-print
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.  ...  For any string s, let σ m (s) be the number of distinct subsequences of s of length m, and let σ(s) be the total number of distinct subsequences.  ...  Subsequences of length m If a string s begins with a run of length k, then we can assume with no loss of generality -since we are only counting distinct subsequences -that every nonempty subsequence starts  ... 
arXiv:1310.7288v1 fatcat:fcbmho2o7vh3vcenfgrryvloda

Algorithms for subsequence combinatorics

Cees Elzinga, Sven Rahmann, Hui Wang
2008 Theoretical Computer Science  
We present theorems that lead to efficient dynamic programming algorithms to count (1) distinct subsequences in a string, (2) distinct common subsequences of two strings, (3) matching joint embeddings  ...  in two strings, (4) distinct subsequences with a given minimum span, and (5) sequences generated by a string allowing characters to come in runs of a length that is bounded from above.  ...  Counting distinct subsequences In this section, we present an efficient solution to the problem of counting all distinct subsequences of length k ≥ 0 of a given string, and study strings that have maximally  ... 
doi:10.1016/j.tcs.2008.08.035 fatcat:ktppztjfsrcnnnzoe57434v37i

Counting Colours in Compressed Strings [article]

Travis Gagie, Juha Kärkkäinen
2010 arXiv   pre-print
Suppose we are asked to preprocess a string s [1..n] such that later, given a substring's endpoints, we can quickly count how many distinct characters it contains.  ...  Storing these points is equivalent to storing a string s [1. .n] over an alphabet whose size σ is the number of distinct colours, such that later, given a substring's endpoints, we can quickly count how  ...  Given a string s[1. .n], we can build a data structure that takes (1 + o(1))(n log σ + n log log n) bits such that later, given a substring's endpoints, in O(log n) time we can count how many distinct  ... 
arXiv:1011.3480v1 fatcat:2xlsiuvafbgmnmmau4njcaca4a

Counting Suffix Arrays and Strings [chapter]

Klaus-Bernd Schürmann, Jens Stoye
2005 Lecture Notes in Computer Science  
Strings sharing the same suffix array are counted in Section 4 and distinct suffix arrays in Section 5.  ...  For fixed alphabet size and string length we count the number of strings sharing the same suffix array and the number of such suffix arrays.  ...  Theorem 4.5 gave the number of distinct strings, and for the order-distinct strings we just sum up over all possible k. Counting suffix arrays for strings with fixed alphabet.  ... 
doi:10.1007/11575832_8 fatcat:biini72fhbcctngchiwf2vyuri

Repetitions in strings: Algorithms and combinatorics

Maxime Crochemore, Lucian Ilie, Wojciech Rytter
2009 Theoretical Computer Science  
For example we know that the number of (distinct) primitivelyrooted squares in a string of length n is no more than 2n − Θ(log n), conjecture to be n, and that their number of occurrences can be Θ(n log  ...  For these repetitions, we distinguish between the factors (sometimes qualified as distinct) and their occurrences (also called positioned factors).  ...  As we shall see, counting distinct squares, i.e. squares that are distinct strings, or squares occurrences gives very different results.  ... 
doi:10.1016/j.tcs.2009.08.024 fatcat:w7oobojrdfcvvirqaldgptnxie

Counting Lyndon Subsequences [article]

Ryo Hirakawa, Yuto Nakashima, Shunsuke Inenaga, Masayuki Takeda
2021 arXiv   pre-print
We show (1) the maximum total number of Lyndon subsequences in a string, (2) the expected total number of Lyndon subsequences in a string, (3) the expected number of distinct Lyndon subsequences in a string  ...  In this paper, we consider a more general problem "counting Lyndon subsequences".  ...  of distinct Lyndon subsequences in all strings of length n over an alphabet Σ of size σ.  ... 
arXiv:2106.01190v2 fatcat:oo52mxpqefd7zkvygkt4itpbeu

RDFStats - An Extensible RDF Statistics Generator and Library

Andreas Langegger, Wolfram Woss
2009 2009 20th International Workshop on Database and Expert Systems Application  
The first one uses a histogram bin for all distinct values and counts the occurrences of equal strings.  ...  Fig. 1 . 1 |u| = COUNT(*) { [] a c } for (c : classes) more c get list of properties used with c props = DISTINCT { [] a c ; ?  ... 
doi:10.1109/dexa.2009.25 dblp:conf/dexaw/LangeggerW09 fatcat:nszrp5djyvft3eu53hlr4sxoim

Distinctive patterns in the first movement of Brahms' String Quartet in C minor

Darrell Conklin
2010 Journal of Mathematics and Music - Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance  
The method is applied to the first movement of Brahms' string quartet No. 1 in C Minor, with the first movements of string quartets Nos. 2 and 3 used as an anticorpus.  ...  In this paper a computational inductive method for maximally general distinctive pattern discovery in music is developed.  ...  Each node contains a pattern, its total count, and its distinctiveness.  ... 
doi:10.1080/17459737.2010.515421 fatcat:fpuc4vfxsrhltkl6fbstgco3wi

PPDC: A Privacy-Preserving Distinct Counting Scheme for Mobile Sensing

Xiaochen Yang, Ming Xu, Shaojing Fu, Yuchuan Luo
2019 Applied Sciences  
In this paper, we propose a Privacy-Preserving Distinct Counting scheme (PPDC) for mobile sensing.  ...  Among major mobile sensing applications, the distinct counting problem aiming to find the number of distinct elements in a data stream with repeated elements, is extremely important for avoiding waste  ...  Distinct Counting On the other hand, distinct counting is also of interest to a lot of researches.  ... 
doi:10.3390/app9183695 fatcat:wfe4mwcnpjdspjdqqqbdpwmjjq

Lower Bounds for the Number of Repetitions in 2D Strings [article]

Paweł Gawrychowski, Samah Ghazawi, Gad M. Landau
2021 arXiv   pre-print
First, we construct an infinite family of n× n 2D strings with Ω(n^3) distinct tandems. Second, we construct an infinite family of n× n 2D strings with Ω(n^2log n) distinct quartics.  ...  We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.  ...  Of course, any fragment of the string a n is a palindrome, therefore we would like to count distinct palindromes.  ... 
arXiv:2105.14903v1 fatcat:5e2bbap4lvedvgtvgibcdeb5e4

Page 79 of Computational Linguistics Vol. 30, Issue 1 [page]

2004 Computational Linguistics  
In fact, the three- character string |] #U ¥ has three distinct oie “S”, T,% (“S” denotes the start of a sentence), and four distinct suffixes, 3, , {k, J (“E” denotes the termination of a sentence).  ...  Therefore, “S” and “E” will be counted multiple times, and we regard % are probably very rarely other characters prec i. or succeeding it.  ... 

Counting Distinct Patterns in Internal Dictionary Matching

Panagiotis Charalampopoulos, Tomasz Kociumaka, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, Wiktor Zuba, Oren Weimann, Inge Li Gørtz
2020 Annual Symposium on Combinatorial Pattern Matching  
We design an 𝒪(n log² n)-size data structure that allows us to count distinct squares in a text fragment T[i..j] in 𝒪(log n) time.  ...  We also consider the special case when the dictionary consists of all square factors of the string.  ...  Counting Distinct Patterns in Internal Dictionary Matching We now proceed to np-squares.  ... 
doi:10.4230/lipics.cpm.2020.8 dblp:conf/cpm/Charalampopoulos20 fatcat:3pzibawykvd53nxmgbpepnme64

Counting Distinct Patterns in Internal Dictionary Matching [article]

Panagiotis Charalampopoulos, Tomasz Kociumaka, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, Wiktor Zuba
2020 arXiv   pre-print
We design an O(n log^2 n)-size data structure that allows us to count distinct squares in a text fragment T[i . . j] in O(log n) time.  ...  We also consider the special case when the dictionary consists of all square factors of the string.  ...  Query: CountDistinct(i, j): Count all distinct patterns P ∈ D that occur in T [i . . j]. Observe that the input size is n + d, while the total length of strings in D could be Θ(n · d).  ... 
arXiv:2005.05681v1 fatcat:qsxkfbjmdbaezil3dbif5vslwm
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