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Counting Distinct Strings

1999
*
Algorithmica
*

This paper discusses how to

doi:10.1007/pl00009247
fatcat:d4ywnnm4hbarjmlsfgyebclvpa
*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*. ...##
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Counting suffix arrays and strings

2008
*
Theoretical Computer Science
*

For each such equivalence class, we

doi:10.1016/j.tcs.2008.01.011
fatcat:tqb7fk5inrgpfjdhd6uibqkfb4
*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. ...##
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The Number of Distinct Subsequences of a Random Binary String
[article]

2013
*
arXiv
*
pre-print

We determine the average number of

arXiv:1310.7288v1
fatcat:fcbmho2o7vh3vcenfgrryvloda
*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 ...##
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Algorithms for subsequence combinatorics

2008
*
Theoretical Computer Science
*

We present theorems that lead to efficient dynamic programming algorithms to

doi:10.1016/j.tcs.2008.08.035
fatcat:ktppztjfsrcnnnzoe57434v37i
*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 ...##
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Counting Colours in Compressed Strings
[article]

2010
*
arXiv
*
pre-print

Suppose we are asked to preprocess a

arXiv:1011.3480v1
fatcat:2xlsiuvafbgmnmmau4njcaca4a
*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*...##
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Counting Suffix Arrays and Strings
[chapter]

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. ...

##
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Repetitions in strings: Algorithms and combinatorics

2009
*
Theoretical Computer Science
*

For example we know that the number of (

doi:10.1016/j.tcs.2009.08.024
fatcat:w7oobojrdfcvvirqaldgptnxie
*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. ...##
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Counting Lyndon Subsequences
[article]

2021
*
arXiv
*
pre-print

We show (1) the maximum total number of Lyndon subsequences in a

arXiv:2106.01190v2
fatcat:oo52mxpqefd7zkvygkt4itpbeu
*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. ...##
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RDFStats - An Extensible RDF Statistics Generator and Library

2009
*
2009 20th International Workshop on Database and Expert Systems Application
*

The first one uses a histogram bin for all

doi:10.1109/dexa.2009.25
dblp:conf/dexaw/LangeggerW09
fatcat:nszrp5djyvft3eu53hlr4sxoim
*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 ; ? ...##
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Distinctive patterns in the first movement of Brahms' String Quartet in C minor

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'

doi:10.1080/17459737.2010.515421
fatcat:fpuc4vfxsrhltkl6fbstgco3wi
*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*. ...##
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PPDC: A Privacy-Preserving Distinct Counting Scheme for Mobile Sensing

2019
*
Applied Sciences
*

In this paper, we propose a Privacy-Preserving

doi:10.3390/app9183695
fatcat:wfe4mwcnpjdspjdqqqbdpwmjjq
*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. ...##
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Lower Bounds for the Number of Repetitions in 2D Strings
[article]

2021
*
arXiv
*
pre-print

First, we construct an infinite family of n× n 2D

arXiv:2105.14903v1
fatcat:5e2bbap4lvedvgtvgibcdeb5e4
*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. ...##
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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. ...##
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Counting Distinct Patterns in Internal Dictionary Matching

2020
*
Annual Symposium on Combinatorial Pattern Matching
*

We design an 𝒪(n log² n)-size data structure that allows us to

doi:10.4230/lipics.cpm.2020.8
dblp:conf/cpm/Charalampopoulos20
fatcat:3pzibawykvd53nxmgbpepnme64
*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. ...##
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Counting Distinct Patterns in Internal Dictionary Matching
[article]

2020
*
arXiv
*
pre-print

We design an O(n log^2 n)-size data structure that allows us to

arXiv:2005.05681v1
fatcat:qsxkfbjmdbaezil3dbif5vslwm
*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). ...
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