An introduction to the analysis of algorithms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
[2018]
|
| Ausgabe: | 3rd edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xv, 312 Seiten Diagramme |
| ISBN: | 9789813235908 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to the analysis of algorithms |c Michael Soltys, California State University Channel Islands, USA. |
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| 264 | 1 | |a New Jersey |b World Scientific |c [2018] | |
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Datensatz im Suchindex
| _version_ | 1804178601150513152 |
|---|---|
| adam_text | Contents
Preface vii
1. Preliminaries 1
1.1 What is correctness?..................................... 1
1.1.1 Complexity........................................ 3
1.1.2 Division ......................................... 4
1.1.3 Euclid ........................................... 5
1.1.4 Palindromes...................................... 7
1.1.5 Further examples.................................. 9
1.2 Ranking algorithms..................................... 11
1.2.1 PageRank........................................ 11
1.2.2 A stable marriage................................ 14
1.2.3 Pairwise Comparisons............................ 17
1.3 Answers to selected problems........................... 19
1.4 Notes .................................................. 26
2. Greedy Algorithms 29
2.1 Minimum cost spanning trees........................... 29
2.2 Jobs with deadlines and profits........................ 37
2.3 Further examples and problems........................... 40
2.3.1 Make-change...................................... 40
2.3.2 Maximum weight matching.......................... 41
2.3.3 Shortest path .................................. 41
2.3.4 Huffman codes.................................... 45
2.4 Answers to selected problems......................... . 47
2.5 Notes................................................... 54
xi
Xll
An introduction to the analysis of algorithms
3. Divide and Conquer 57
3.1 Mergesort ................................................ 58
3.2 Multiplying numbers in binary............................. 59
3.3 Savitch’s algorithm....................................... 62
3.4 Further examples and problems............................. 64
3.4.1 Extended Euclid’s algorithm....................... 64
3.4.2 Quicksort......................................... 65
3.4.3 Git bisect........................................ 66
3.5 Answers to selected problems.............................. 66
3.6 Notes.................................................... 68
4. Dynamic Programming 71
4.1 Longest monotone subsequence problem...................... 71
4.2 All pairs shortest path problem........................... 73
4.2.1 Bellman-Ford algorithm............................ 74
4.3 Simple knapsack problem................................... 75
4.3.1 Dispersed knapsack problem........................ 78
4.3.2 General knapsack problem......................... 79
4.4 Activity selection problem................................ 80
4.5 Jobs with deadlines, durations and profits................ 82
4.6 Further examples and problems............................. 84
4.6.1 Consecutive subsequence sum problem ...... 84
4.6.2 Shuffle.......................................... 85
4.7 Answers to selected problems.............................. 87
4.8 Notes .................................................... 92
5. Online Algorithms 95
5.1 List accessing problem . . . ............................. 96
5.2 Paging.................................................. 100
5.2.1 Demand paging................................... 101
5.2.2 FIFO............................................. 104
5.2.3 LRU............................................. 104
5.2.4 Marking algorithms............................... 108
5.2.5 FWF.............................................. 109
5.2.6 LFD ............................................. 110
5.3 Answers to selected problems . ......................... 114
5.4 Notes ................................................... 118
Contents xiii
6. Randomized Algorithms 119
6.1 Perfect matching........................................ 120
6.2 Pattern matching........................................ 124
6.3 Primality testing....................................... 126
6.4 Public key cryptography................................ 129
6.4.1 Diffie-Hellman key exchange..................... 130
6.4.2 ElGamal......................................... 133
6.4.3 RSA ............................................ 135
6.5 Further problems........................................ 137
6.6 Answers to selected problems............................ 138
6.7 Notes ................................................. 144
7. Algorithms in Linear Algebra 149
7.1 Introduction............................................ 149
7.2 Gaussian Elimination .................................. 150
7.2.1 Formal proofs of correctness over Z2............ 153
7.3 Gram-Schmidt............................................ 156
7.4 Gaussian lattice reduction.............................. 157
7.5 Computing the characteristic polynomial................. 157
7.5.1 Csanky’s algorithm.............................. 158
7.5.2 Berkowitz’s algorithm.......................... 158
7.5.3 Proving properties of the characteristic polynomial 159
7.6 Answers to selected problems............................ 166
7.7 Notes .................................................. 169
8. Computational Foundations 171
8.1 Introduction............................................ 171
8.2 Alphabets, strings and languages........................ 172
8.3 Regular languages....................................... 173
8.3.1 Deterministic Finite Automaton.................. 173
8.3.2 Nondeterministic Finite Automata................ 176
8.3.3 Regular Expressions............................. 179
8.3.4 Algebraic laws for Regular Expressions.......... 182
8.3.5 Closure properties of regular languages......... 184
8.3.6 Complexity of transformations and decisions ... 184
8.3.7 Equivalence and minimization of automata .... 185
8.3.8 Languages that are not regular................. 186
8.3.9 Automata on terms............................... 189
XIV
An introduction to the analysis of algorithms
8.4 Context-free languages.................................. 190
8.4.1 Context-free grammars............................ 190
8.4.2 Pushdown automata................................ 192
8.4.3 Chomsky Normal Form.............................. 195
8.4.4 CYK algorithm.................................... 197
8.4.5 Pumping Lemma for CFLs........................... 198
8.4.6 Further observations about CFL ................. 199
8.4.7 Other grammars.................................. 200
8.5 Turing machines......................................... 201
8.5.1 Nondeterministic TMs ............................ 202
8.5.2 Encodings........................................ 203
8.5.3 Decidability..................................... 204
8.5.4 Church-Turing thesis............................. 205
8.5.5 Undecidability................................... 206
8.5.6 Reductions........................................208
8.5.7 Rice’s theorem................................... 209
8.5.8 Post’s Correspondence Problem.................... 209
8.5.9 Undecidable properties of CFLs....................215
8.6 Answers to selected problems..............................217
8.7 Notes .................................................. 229
9. Mathematical Foundations 231
9.1 Induction and Invariance................................. 231
9.1.1 Induction........................................ 231
9.1.2 Invariance....................................... 234
9.2 Number Theory........................................... 236
9.2.1 Prime numbers.................................... 236
9.2.2 Modular arithmetic............................... 237
9.2.3 Group theory.................................... 239
9.2.4 Applications of group theory to number theory . . 240
9.3 Relations................................................ 242
9.3.1 Closure.......................................... 243
9.3.2 Equivalence relation............................. 244
9.3.3 Partial orders................................... 246
9.3.4 Lattices......................................... 248
9.3.5 Fixed point theory............................... 250
9.3.6 Recursion and fixed points....................... 254
9.4 Logic.................................................... 256
9.4.1 Propositional logic . . . ................ . . . 256
Contents xv
9.4.2 First Order Logic....................................262
9.4.3 Peano Arithmetic.....................................267
9.4.4 Formal verification ................................ 268
9.5 Answers to selected problems.................................271
9.6 Notes...................................................... 292
Bibliography 295
Index 303
|
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| dewey-ones | 518 - Numerical analysis |
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| dewey-sort | 3518 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 3rd edition |
| format | Book |
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| spelling | Soltys, Michael 1971- (DE-588)1075056675 aut An introduction to the analysis of algorithms Michael Soltys, California State University Channel Islands, USA. 3rd edition New Jersey World Scientific [2018] xv, 312 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Algorithms Textbooks Beweis (DE-588)4132532-1 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Programmanalyse (DE-588)4175841-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algorithmus (DE-588)4001183-5 s Beweis (DE-588)4132532-1 s DE-604 Programmanalyse (DE-588)4175841-9 s 1\p DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030390479&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Soltys, Michael 1971- An introduction to the analysis of algorithms Algorithms Textbooks Beweis (DE-588)4132532-1 gnd Algorithmus (DE-588)4001183-5 gnd Programmanalyse (DE-588)4175841-9 gnd |
| subject_GND | (DE-588)4132532-1 (DE-588)4001183-5 (DE-588)4175841-9 (DE-588)4151278-9 |
| title | An introduction to the analysis of algorithms |
| title_auth | An introduction to the analysis of algorithms |
| title_exact_search | An introduction to the analysis of algorithms |
| title_full | An introduction to the analysis of algorithms Michael Soltys, California State University Channel Islands, USA. |
| title_fullStr | An introduction to the analysis of algorithms Michael Soltys, California State University Channel Islands, USA. |
| title_full_unstemmed | An introduction to the analysis of algorithms Michael Soltys, California State University Channel Islands, USA. |
| title_short | An introduction to the analysis of algorithms |
| title_sort | an introduction to the analysis of algorithms |
| topic | Algorithms Textbooks Beweis (DE-588)4132532-1 gnd Algorithmus (DE-588)4001183-5 gnd Programmanalyse (DE-588)4175841-9 gnd |
| topic_facet | Algorithms Textbooks Beweis Algorithmus Programmanalyse Einführung |
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