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Finding all periods and initial palindromes of a string in parallel

D. Breslauer, Z. Galil
1995 Algorithmica  
The algorithm can be used to find all initial palindromes of a string in the same time and processor bounds. Both algorithms are the fastest possible over a general alphabet.  ...  We derive a lower bound for finding initial palindromes by modifying a known lower bound for finding the period length of a string [9] .  ...  We also thank Alberto Apostolico, Roberto Grossi, JOrg Keller, Kunsoo Park, and Laura Toniolo for comments on early versions of this paper. 366 D. Breslauer and z. Gali!  ... 
doi:10.1007/bf01294132 fatcat:pqu6udrmrfe7jdka6jwgshyjwy

Efficient string matching on packed texts

D. Breslauer, Leszek Gasieniec
1996 RAIRO - Theoretical Informatics and Applications  
ACKNOWLEDGMENTS We thank Pierre Kelsen and Thierry Lecroq for the French translation of the abstract. Special thanks are to Faith Fich for her helpfull comments on the final version of the paper.  ...  is square-free and for finding all palindromes in a string.  ...  The lower bound was later generalized by Breslauer and Galil [13] to other string problems like finding all periods and initial palindromes of a given string. Recently Breslauer et al.  ... 
doi:10.1051/ita/1996300605211 fatcat:v57knovkdjd6zapxyohcih4u4e

Efficient String Matching on Coded Texts

Dany Breslauer
1994 BRICS Report Series  
Using this string-matching algorithm one can test if a string is square-free and find all palindromes in a string in O(log log n) time using n / log log n processors.  ...  of lambda = O(log n) on the number of operations used in previous algorithms.  ...  is square-free and for finding all palindromes in a string.  ... 
doi:10.7146/brics.v1i42.21600 fatcat:37xqa3grlvcf7j6lfuqbf533ge

Efficient string matching on coded texts [chapter]

Dany Breslauer, Leszek Gasieniec
1995 Lecture Notes in Computer Science  
Apostolico, Breslauer and Galil gave efficient parallel algorithms for testing if a string is square-free and for finding all palindromes in a string [4, 5, 6] .  ...  The string-matching algorithm is given is Section 4 and its applications for testing if a string is square-free and for finding all palindromes in a string are given in Section 5.  ...  is square-free and for finding all palindromes in a string.  ... 
doi:10.1007/3-540-60044-2_32 fatcat:yi2mwncrwbcs7mgwyhoapywsxu

Page 3741 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
(NL-MATH; Amsterdam); Galil, Z. (1-CLMB-C; New York, NY) Finding all periods and initial palindromes of a string in parallel. (English summary) Algorithmica 14 (1995), no. 4, 355-366.  ...  We derive a lower bound for finding initial palindromes by modifying a known lower bound for finding the period length of a string [D. Breslauer and Z. Galil, SIAM J.  ... 

Palindrome recognition in real time by a multitape turing machine

Zvi Galil
1978 Journal of computer and system sciences (Print)  
Using the FPP (the linear-time off-line procedure which finds all intial palindromes in a given string [S]), we find the largest initial palindrome in [L, RIR.  ...  (The close relative, the set {X [ x = wcwR, w E Z+}, of P' is a deterministic cfl.) ProbEem 2. To find all initial palindromes in a given string.  ...  which is called whenever an initial even palindrome is found. This obviously works in the case of a RAM. It works also in the case of a Turing machine.  ... 
doi:10.1016/0022-0000(78)90042-9 fatcat:cmm7zorivzctzcwxjiklhr2xgi

Usefulness of the Karp-Miller-Rosenberg algorithm in parallel computations on strings and arrays

Maxime Crochemore, Wojciech Rytter
1991 Theoretical Computer Science  
The representation of the set of basic factors (subarrays) of a string (array) produced by the algorithm is an extremely useful data structure in parallel algorithms on strings and arrays.  ...  Also the following problems for strings can be solved within the same complexity bounds: finding squares, testing even palstars and compositions of k palindromes for k=2, 3, 4, computing Lyndon factorization  ...  The initial level of the recursion is the zero level, the last one has depth log(n)- Assume that all entries of all tables are initially set to infinity.  ... 
doi:10.1016/0304-3975(91)90073-b fatcat:jbx6jutgdjdp3k7m7eczk3htfi

Efficient computation of maximal anti-exponent in palindrome-free strings

Golnaz Badkobeh, Maxime Crochemore, Manal Mohamed, Chalita Toopsuwan
2016 Theoretical Computer Science  
To get an efficient computation of maximal anti-exponent of factors in a palindrome-free string, we apply techniques based on the suffix automaton and the reversed Lempel-Ziv factorisation.  ...  We consider gapped palindromes which are strings of the form uv u, where u, v are strings, |v| ≥ 2, and u is the reversal of u.  ...  Early studies by Manacher [16] and Galil [10] contributed to the construction of linear-time algorithms to find palindromes in a string.  ... 
doi:10.1016/j.tcs.2016.02.014 fatcat:zqx4pxgipvallh35w3ldymifxe

An Efficient Implementation of Manacher's Algorithm [article]

Shoupu Wan
2020 arXiv   pre-print
Many of the existing implementations of this algorithm, however, unanimously required in-memory construction of an augmented string that is twice as long as the original string.  ...  We present a more efficient implementation of Manacher's algorithm based on index mapping that makes the string augmentation process obsolete.  ...  Introduction Finding a longest palindrome substring (LPS) in a given string is a fundamentally important question as it has widespread applications in mathematics, physics, chemistry, genetics, music,  ... 
arXiv:2003.08211v2 fatcat:avqsxiiyyfajjaa3pq2blxckx4

Page 2056 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
[Chen, Hsiu-Niang] Parallel finding all initial palindromes and periods of a string on reconfigurable meshes. (English summary) Computing 61 (1998), no. 1, 11-21.  ...  Summary: “Given a string of length n, this short paper first presents an O(1)-time parallel algorithm for finding all initial palindromes and periods of the string on an nxn _ recon- figurable mesh (RM  ... 

Optimal parallel algorithms for string matching

Zvi Galil*
1984 Proceedings of the sixteenth annual ACM symposium on Theory of computing - STOC '84  
Similar families are also obtained for the problem of finding all initial palindromes of a given string.  ...  We design below families of p~rallel algorithms that solve the string matching problem with inputs of size n (n is the sum of lengths of the pattern and the text) and have the following performance in  ...  ACKNOWLEDGMENTS I am indebted to Uzi Vishkin for suggestions that have led to several improvements, and to Stuart Haber and Glenn Manacher for many suggestions concerning the presentation.  ... 
doi:10.1145/800057.808687 dblp:conf/stoc/Galil84 fatcat:kjo6oscm3vbzpnc3ysy6wlacda

Optimal parallel algorithms for string matching

Zvi Galil
1985 Information and Control  
Similar families are also obtained for the problem of finding all initial palindromes of a given string.  ...  We design below families of p~rallel algorithms that solve the string matching problem with inputs of size n (n is the sum of lengths of the pattern and the text) and have the following performance in  ...  ACKNOWLEDGMENTS I am indebted to Uzi Vishkin for suggestions that have led to several improvements, and to Stuart Haber and Glenn Manacher for many suggestions concerning the presentation.  ... 
doi:10.1016/s0019-9958(85)80031-0 fatcat:ltclehvuazb5zclomy72mq6udm

Palindrome Recognition In The Streaming Model

Petra Berenbrink, Funda Ergün, Frederik Mallmann-Trenn, Erfan Sadeqi Azer, Marc Herbstritt
2014 Symposium on Theoretical Aspects of Computer Science  
In the Palindrome Problem, one tries to find all palindromes in a given string.  ...  In contrast, in the case of the Longest Palindromic Substring Problem, the goal is to find an arbitrary one of the longest palindromes in the string.  ...  Lemma 17 and Lemma 18 yield the claimed space. In every iteration the algorithm processes every checkpoint in CL i in constant time. The number of checkpoints is bounded by Lemma 17.  ... 
doi:10.4230/lipics.stacs.2014.149 dblp:conf/stacs/BerenbrinkEMA14 fatcat:fx6kspplbbay5opg3bf34pxoly

One-way bounded cellular automata

Charles R. Dyer
1980 Information and Control  
This paper studies a restriction of one-dimensional bounded cellular automata in which information is allowed to move only in one direction.  ...  Real-time aeceptors are presented for many of the languages that have been shown to he accepted by conventional two-way acceptors, including several classes of context-free languages.  ...  M accepts a string a e (Q~ --{#}) if M has initial configuration #~a# °:, and at some time step M's rightmust non-# cell, the accepting cell, enters a state in Q,4 • The set of strings accepted by M defines  ... 
doi:10.1016/s0019-9958(80)90164-3 fatcat:m5qjdqpmgrcmrd4f3b2t5grxae

Palindrome Recognition In The Streaming Model [article]

Petra Berenbrink, Funda Ergün, Frederik Mallmann-Trenn, Erfan Sadeqi Azer
2016 arXiv   pre-print
In the Palindrome Problem one tries to find all palindromes (palindromic substrings) in a given string.  ...  A related problem is the Longest Palindromic Substring Problem in which finding an arbitrary one of the longest palindromes in the given string suffices.  ...  The authors of [1] show how to modify this algorithm in order to find all palindromic substrings in linear time (using a parallel algorithm).  ... 
arXiv:1308.3466v3 fatcat:th6ed5xp3fblrltpjtajlcwup4
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