125 Problems in Text Algorithms: with Solutions

345 Pages·2021·9.756 MB·English

by  Maxime Crochemore, Thierry Lecroq, Wojciech Rytter

125ProblemsinTextAlgorithms
Stringmatchingisoneoftheoldestalgorithmictechniques,yetstilloneofthemost
pervasiveincomputerscience.Thepast20yearshaveseentechnologicalleapsin
applicationsasdiverseasinformationretrievalandcompression.Thiscopiously
illustratedcollectionofpuzzlesandexercisesinkeyareasoftextalgorithmsand
combinatoricsonwordsoffersgraduatestudentsandresearchersapleasantanddirect
waytolearnandpracticewithadvancedconcepts.
Theproblemsaredrawnfromalargerangeofscientificpublications,bothclassic
andnew.Buildingupfromthebasics,thebookgoesontoshowcaseproblemsin
combinatoricsonwords(includingFibonacciorThue–Morsewords),pattern
matching(includingKnuth–Morris–PrattandBoyer–Moore–likealgorithms),efficient
textdatastructures(includingsuffixtreesandsuffixarrays),regularitiesinwords
(includingperiodsandruns)andtextcompression(includingHuffman,Lempel–Ziv
andBurrows–Wheeler–basedmethods).
Maxime CrochemoreisEmeritusProfessoratUniversitéGustaveEiffeland
ofKing’sCollegeLondon.HeholdsanhonorarydoctoratefromtheUniversityof
Helsinki.Heistheauthorofmorethan200articlesonalgorithmsonstringsandtheir
applications,andco-authorofseveralbooksonthesubject.
Thierry LecroqisaprofessorintheDepartmentofComputerScienceatthe
UniversityofRouenNormandy(France).Heiscurrentlyheadoftheresearchteam
InformationProcessinginBiologyandHealthoftheLaboratoryofComputerScience,
InformationProcessingandSystem.Hehasbeenoneofthecoordinatorsofthe
workinggroupinstringologyoftheFrenchNationalCentreforScientificResearchfor
morethan10years.
Wojciech RytterisaprofessorattheFacultyofMathematics,Informatics
andMechanics,UniversityofWarsaw.Heistheauthorofalargenumberof
publicationsonautomata,formallanguages,parallelalgorithmsandalgorithmson
texts.Heisaco-authorofseveralbooksonthesesubjects,includingEfficientParallel
Algorithms,TextAlgorithmsandAnalysisofAlgorithmsandDataStructures.Heisa
memberofAcademiaEuropaea.

125 Problems in Text Algorithms
With Solutions
MAXIME CROCHEMORE
GustaveEiffelUniversity
THIERRY LECROQ
UniversityofRouenNormandy
WOJCIECH RYTTER
UniversityofWarsaw
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108835831
DOI:10.1017/9781108869317
©MaximeCrochemore,ThierryLecroq,WojciechRytter2021
IllustrationsdesignedbyHélèneCrochemore
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
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Firstpublished2021
PrintedintheUnitedKingdombyTJBooksLtd,PadstowCornwall
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Crochemore,Maxime,1947–author.|Lecroq,Thierry,author.|
Rytter,Wojciech,author.
Title:Onetwentyfiveproblemsintextalgorithms/MaximeCrochemore,
ThierryLecroq,WojciechRytter.
Othertitles:125problemsintextalgorithms
Description:NewYork:CambridgeUniversityPress,2021.|
Thenumerals125aresuperimposedover“Onetwentyfive”onthetitlepage.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2021002037(print)|LCCN2021002038(ebook)|
ISBN9781108835831(hardback)|ISBN9781108798853(paperback)|
ISBN9781108869317(epub)
Subjects:LCSH:Textprocessing(Computerscience)–Problems,exercises,etc.|
Computeralgorithms–Problems,exercises,etc.
Classification:LCCQA76.9.T48C7582021(print)|
LCCQA76.9.T48(ebook)|DDC005.13–dc23
LCrecordavailableathttps://lccn.loc.gov/2021002037
LCebookrecordavailableathttps://lccn.loc.gov/2021002038
ISBN978-1-108-83583-1Hardback
ISBN978-1-108-79885-3Paperback
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Contents
Preface pageix
1 TheVeryBasicsofStringology 1
2 CombinatorialPuzzles 17
1 StringologicProofofFermat’sLittleTheorem 18
2 SimpleCaseofCodicityTesting 19
3 MagicSquaresandtheThue–MorseWord 20
4 Oldenburger–KolakoskiSequence 22
5 Square-FreeGame 24
6 FibonacciWordsandFibonacciNumerationSystem 26
7 Wythoff’sGameandFibonacciWord 28
8 DistinctPeriodicWords 30
9 ARelativeoftheThue–MorseWord 33
10 Thue–MorseWordsandSumsofPowers 34
11 ConjugatesandRotationsofWords 35
12 ConjugatePalindromes 37
13 ManyWordswithManyPalindromes 39
14 ShortSuperwordofPermutations 41
15 ShortSupersequenceofPermutations 43
16 SkolemWords 45
17 LangfordWords 48
18 FromLyndonWordstodeBruijnWords 50
3 PatternMatching 53
19 BorderTable 54
20 ShortestCovers 56
21 ShortBorders 58
v
vi Contents
22 PrefixTable 60
23 BorderTabletotheMaximalSuffix 62
24 PeriodicityTest 65
25 StrictBorders 67
26 DelayofSequentialStringMatching 70
27 SparseMatchingAutomaton 72
28 Comparison-EffectiveStringMatching 74
29 StrictBorderTableoftheFibonacciWord 76
30 WordswithSingletonVariables 78
31 Order-PreservingPatterns 81
32 ParameterisedMatching 83
33 Good-SuffixTable 85
34 WorstCaseoftheBoyer–MooreAlgorithm 88
35 Turbo-BMAlgorithm 90
36 StringMatchingwithDon’tCares 92
37 CyclicEquivalence 93
38 SimpleMaximalSuffixComputation 96
39 Self-MaximalWords 98
40 MaximalSuffixandItsPeriod 100
41 CriticalPositionofaWord 103
42 PeriodsofLyndonWordPrefixes 105
43 SearchingZiminWords 107
44 SearchingIrregular2DPatterns 110
4 EfficientDataStructures 111
45 ListAlgorithmforShortestCover 112
46 ComputingLongestCommonPrefixes 113
47 SuffixArraytoSuffixTree 115
48 LinearSuffixTrie 119
49 TernarySearchTrie 122
50 LongestCommonFactorofTwoWords 124
51 SubsequenceAutomaton 126
52 CodicityTest 128
53 LPFTable 130
54 SortingSuffixesofThue–MorseWords 134
55 BareSuffixTree 137
56 ComparingSuffixesofaFibonacciWord 139
57 AvoidabilityofBinaryWords 141
58 AvoidingaSetofWords 144
vii
59 MinimalUniqueFactors 146
60 MinimalAbsentWords 148
61 GreedySuperstring 152
62 ShortestCommonSuperstringofShortWords 155
63 CountingFactorsbyLength 157
64 CountingFactorsCoveringaPosition 160
65 LongestCommon-ParityFactors 161
66 WordSquare-FreenesswithDBF 162
67 GenericWordsofFactorEquations 164
68 SearchinganInfiniteWord 166
69 PerfectWords 169
70 DenseBinaryWords 173
71 FactorOracle 175
5 RegularitiesinWords 180
72 ThreeSquarePrefixes 181
73 TightBoundsonOccurrencesofPowers 183
74 ComputingRunsonGeneralAlphabets 185
75 TestingOverlapsinaBinaryWord 188
76 Overlap-FreeGame 190
77 AnchoredSquares 192
78 AlmostSquare-FreeWords 195
79 BinaryWordswithFewSquares 197
80 BuildingLongSquare-FreeWords 199
81 TestingMorphismSquare-Freeness 201
82 NumberofSquareFactorsinLabelledTrees 203
83 CountingSquaresinCombsinLinearTime 206
84 CubicRuns 208
85 ShortSquareandLocalPeriod 210
86 TheNumberofRuns 212
87 ComputingRunsonSortedAlphabet 214
88 PeriodicityandFactorComplexity 219
89 PeriodicityofMorphicWords 220
90 SimpleAnti-powers 222
91 PalindromicConcatenationofPalindromes 224
92 PalindromeTrees 225
93 UnavoidablePatterns 227
viii Contents
6 TextCompression 230
94 BWTransformofThue–MorseWords 231
95 BWTransformofBalancedWords 233
96 In-placeBWTransform 237
97 Lempel–ZivFactorisation 239
98 Lempel–Ziv–WelchDecoding 242
99 CostofaHuffmanCode 244
100 Length-LimitedHuffmanCoding 248
101 OnlineHuffmanCoding 253
102 Run-LengthEncoding 256
103 ACompactFactorAutomaton 261
104 CompressedMatchinginaFibonacciWord 264
105 PredictionbyPartialMatching 266
106 CompressingSuffixArrays 269
107 CompressionRatioofGreedySuperstrings 271
7 Miscellaneous 275
108 BinaryPascalWords 276
109 Self-ReproducingWords 278
110 WeightsofFactors 280
111 Letter-OccurrenceDifferences 282
112 FactoringwithBorder-FreePrefixes 283
113 PrimitivityTestforUnaryExtensions 286
114 PartiallyCommutativeAlphabets 288
115 GreatestFixed-DensityNecklace 290
116 Period-EquivalentBinaryWords 292
117 OnlineGenerationofdeBruijnWords 295
118 RecursiveGenerationofdeBruijnWords 298
119 WordEquationswithGivenLengthsofVariables 300
120 DiverseFactorsoveraThree-LetterAlphabet 302
121 LongestIncreasingSubsequence 304
122 UnavoidableSetsviaLyndonWords 306
123 SynchronisingWords 309
124 Safe-OpeningWords 311
125 SuperwordsofShortenedPermutations 314
Bibliography 318
Index 332
Preface
This book is about algorithms on texts, also called algorithmic stringology.
Text (word, string, sequence) is one of the main unstructured data types and
thesubjectisofvitalimportanceincomputerscience.
Thesubjectisversatilebecauseitisabasicrequirementinmanysciences,
especiallyincomputerscienceandengineering.Thetreatmentofunstructured
data is a very lively area and demands efficient methods owing both to their
presenceinhighlyrepetitiveinstructionsofoperatingsystemsandtothevast
amountofdatathatneedstobeanalysedondigitalnetworksandequipments.
Thelatterisclearforinformationtechnologycompaniesthatmanagemassive
data in their data centres but also holds for most scientific areas beyond
Computerscience.
The book presents a collection of the most interesting representative
problems in stringology. They are introduced in a short and pleasant way
andopendoorstomoreadvancedtopics.Theywereextractedfromhundreds
of serious scientific publications, some of which are more than a hundred
years old and some are very fresh and up to date. Most of the problems are
relatedtoapplicationswhileothersaremoreabstract.Thecorepartofmostof
themisaningeniousshortalgorithmicsolutionexceptforafewintroductory
combinatorialproblems.
This is not just yet another monograph on the subject but a series of
problems(puzzlesandexercises).Itisacomplementtobooksdedicatedtothe
subjectinwhichtopicsareintroducedinamoreacademicandcomprehensive
way.Nevertheless,mostconceptsinthefieldareincludedinthebook,which
fillsamissinggapandisveryexpectedandneeded,especiallyforstudentsand
teachers,asthefirstproblem-solvingtextbookofthedomain.
ix