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Average cost of Duval's algorithm for generating Lyndon words

J. Berstel, M. Pocchiola
1994 Theoretical Computer Science  
Pocchiola, Average cost of Duval's algorithm for generating Lyndon words, Theoretical Computer Science 132 (1994) 415-425.  ...  The average cost of Duval's algorithm for generating all Lyndon words up to a given length in lexicographic order is proved to be asymptotically equal to (q+ l)/(q-l), where 4 is the size of the underlying  ...  The total cost C, of Duval's algorithm for generating all Lyndon words of length at most n is C,=2A,-L,-2n+l and the average cost yn is y*=C,/L,d2A,lL,-1.  ... 
doi:10.1016/0304-3975(94)00013-1 fatcat:zpizusveybbilox2vmwzg5bwvi

Page 4910 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
{For the entire collection see MR 95b:68004. } 95h:68147 68R15 68Q25 Berstel, J. (F-PARIS6-BP; Paris); Pocchiola, M. (F-ENS-I; Paris) Average cost of Duval’s algorithm for generating Lyndon words.  ...  The overall time C,, that this algorithm takes for generating all Lyn- don words up to length n is C, = 2A, — L, —2n+1, where L,, is the number of Lyndon words up to length n, and A, = L; + L2+---+L, (  ... 

Space Efficient Construction of Lyndon Arrays in Linear Time [article]

Philip Bille, Jonas Ellert, Johannes Fischer, Inge Li Gørtz, Florian Kurpicz, Ian Munro, Eva Rotenberg
2019 arXiv   pre-print
A simpler variant of this algorithm computes the plain (n n-bit) version of the Lyndon array using only O(1) words of additional working space.  ...  We present the first linear time algorithm to construct the 2n-bit version of the Lyndon array for a string of length n using only o(n) bits of working space.  ...  This can be achieved using a trivial modification of Duval's algorithm for the Lyndon standard factorization[Duval, Now we show that the longest factor in the Lyndon factorization of an extended  ... 
arXiv:1911.03542v2 fatcat:nygmqmb2dncr7nvnpzfrncmuoa

Computation of Maximal Determinants of Binary Circulant Matrices [article]

Richard P. Brent, Adam B. Yedidia
2021 arXiv   pre-print
We describe efficient parallel algorithms for the search, using Duval's algorithm for generation of necklaces and the well-known representation of the determinant of a circulant in terms of roots of unity  ...  We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from {0,1} or {-1,1}.  ...  authors of Magma [8] and GMP [21] for their excellent software.  ... 
arXiv:1801.00399v6 fatcat:wyhmrkie4jc45pypijxbl6lrem

Space Efficient Construction of Lyndon Arrays in Linear Time

Philip Bille, Jonas Ellert, Johannes Fischer, Inge Li Gørtz, Florian Kurpicz, J. Ian Munro, Eva Rotenberg, Emanuela Merelli, Artur Czumaj, Anuj Dawar
2020 International Colloquium on Automata, Languages and Programming  
For the plain (n log₂ n)-bit version, we only need 𝒪(1) additional words to achieve linear time.  ...  While linear time construction algorithms for both representations exist, it has previously been unknown if the same time bound can be achieved with less than Ω(n lg n) bits of additional working space  ...  Using Duval's algorithm [8, Algorithm 2.1], we compute the Lyndon factorization of S in O(n) time and O(1) words of additional space.  ... 
doi:10.4230/lipics.icalp.2020.14 dblp:conf/icalp/BilleE0GKMR20 fatcat:vovgnfe4bzdjneygn36ukpj47i

Near-Optimal Quantum Algorithms for String Problems [article]

Shyan Akmal, Ce Jin
2021 arXiv   pre-print
Our algorithm uses the MNRS quantum walk framework, together with a careful combination of string synchronizing sets (Kempa and Kociumaka, 2019) and generalized difference covers. - Lexicographically Minimal  ...  Our algorithm is an adaptation of the algorithm by Le Gall and Seddighin (2020) for the Longest Palindromic Substring problem, but uses additional techniques to overcome the difficulty that binary search  ...  We additionally thank Virginia Vassilevska Williams for several useful comments on the writeup of this paper.  ... 
arXiv:2110.09696v2 fatcat:v6rindfjrnchbllvjvtcpnalay

Reference list of indexed articles

1995 Theoretical Computer Science  
Pocchiola, Average cost of Duval's algorithm for generating Lyndon words (Note) 132 (l-2) (1994) 415-425 519. L.  ...  Schmid, The average CRl-length of a controlled ALOHA collision resolution algorithm 108 (2) (1993) 291-310 117. R. Bar Yehuda, T. Etzion and S. Moran, Rotating-table games and derivatives of words (.  ... 
doi:10.1016/0304-3975(95)90002-0 fatcat:b7nmywx4tff6lhcd3jkoagotrm

Subject index volumes 101–150

1995 Theoretical Computer Science  
- 624 durations 468, 626, 649 DuvaI 756 Duval's algorithm for Lyndon words, average cost of - 518, 756 average cost of - 518 Dyck paths 2.54 semi--language 5 IX set 420 Dymond and Tompa  ...  - 777 families 768 families, generation of - 768 generation 430, 498 random generation algorithms 498 problem 498 random mappings 7 13 move-to-front I22 NP-complete problem 770  ... 
doi:10.1016/0304-3975(95)80002-6 fatcat:azbu2orp7vc75pwux4jxnvxl7m

Cumulative index volumes 101–150

1995 Theoretical Computer Science  
Pocchiola, Average cost of Duval's algorithm for generating Lyndon words (Note) 132 (l-2) (1994) 415-425 Bertrand, A., Sur une conjecture d'Yves Mettvier 123 E., J. Desel and J.  ...  Seshadri, Efficient sampling strategies for relational database operattons Blot, J., W. Fernandez de la Vega, V.Th. Paschos and R. Saad, Average case analysis of greedy algorithms Brookes, S..  ...  The relationshlp between stable, supported, default and autoepistemic semantics for general logic programs Margenstern.  ... 
doi:10.1016/0304-3975(95)80004-2 fatcat:aobsm3zfjnhhtpd22ucvxasucy

Page 1430 of Mathematical Reviews Vol. 27, Issue Index [page]

Mathematical Reviews  
Average cost of Duval’s algorithm for generating Lyndon words. (English summary) 95h:68147 Bousquet-Mélou, Mireille see Allouche, Jean-Paul, 95m:68132 Carpi, Arturo On repeated factors in C*-words.  ...  (English summary) 95m:68132 Alonso, Laurent Uniform generation of a Motzkin word.  ...