Sorting: a distribution theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley [u.a.]
2000
|
| Schriftenreihe: | Wiley-interscience series in discrete mathematics and optimization
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of Contents Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 373 - 387 |
| Beschreibung: | XIII, 394 S. graph. Darst. |
| ISBN: | 0471327107 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface xi
Acknowledgments xv
1 Sorting and Associated Concepts 1
1.1 Sorting 1
1.2 Selection 2
1.3 Jargon 4
1.4 Algorithmic Conventions 6
1.5 Order 7
1.6 Binary Trees 10
1.7 Decision Trees 18
1.8 Bounds on Sorting 21
1.8.1 Lower Bounds on Sorting 22
1.8.2 Upper Bounds on Sorting 24
1.9 Bounds on Selection 25
1.9.1 Lower Bounds on Selection 26
1.9.2 Upper Bounds on Selection 33
1.10 Random Permutations 36
1.10.1 Records 41
1.10.2 Inversions 44
1.10.3 Cycles 46
1.10.4 Runs 48
1.11 An Analytic Toolkit 53
1.11.1 The Saddle Point Method 54
1.11.2 The Mellin Transform 56
1.11.3 Poissonization 61
1.11.4 The Dirichlet Transform 67
1.11.5 Rice s Method 74
2 Insertion Sort 83
2.1 A General Framework 84
2.2 A Sufficient Condition for Normality 87
vii
viii Contents
2.3 Linear Insertion Sort 88
2.4 Binary Insertion Sort 95
3 Shell Sort 103
3.1 The Algorithm 103
3.2 Streamlined Stochastic Analysis 105
3.2.1 The Empirical Distribution Function 106
3.2.2 The Brownian Bridge 106
3.2.3 Using the Stochastic Tools 114
3.3 Other Increment Sequences 122
4 Bubble Sort 129
4.1 The Algorithm 129
4.2 A limit Law for Passes 131
4.3 A Limit Law for Comparisons 136
5 Selection Sort 139
5.1 The Algorithm 139
5.2 Analysis 140
6 Sorting by Counting 144
6.1 COUNT SORT 144
6.2 Sorting by Counting Frequencies 146
7 Quick Sort 148
7.1 The Partitioning Stage 148
7.2 Bookkeeping 151
7.3 Quick Sort Tree 152
7.4 Probabilistic Analysis of QUICK SORT 153
7.5 Quick Selection 166
7.5.1 Hoare sFIND 167
7.5.2 MULTIPLE QUICK SELECT 177
8 Sample Sort 199
8.1 The Small Sample Algorithm 199
8.2 The Large Sample Algorithm 205
9 Heap Sort 212
9.1 The Heap 212
9.2 Sorting via a Heap 217
Contents ix
10 Merge Sort 220
10.1 Merging Sorted Lists 220
10.1.1 LINEAR MERGE 222
10.1.2 BINARY MERGE 227
10.1.3 The HWANG-LIN Merging Algorithm 228
10.2 The Merge Sort Algorithm 230
10.3 Distributions 239
10.4 Bottom-Up Merge Sort 243
11 Bucket Sorts 250
11.1 The Principle of Bucket Sorting 250
11.1.1 Distributive Sorts 253
11.1.2 Radix Sorting 259
11.2 Bucket Selection 269
11.2.1 Distributive Selection 271
11.2.2 Radix Selection 276
12 Sorting Nonrandom Data 283
12.1 Measures of Presortedness 284
12.2 Data Randomization 284
12.3 Guaranteed Performance 286
12.3.1 The FORD-JOHNSON Algorithm 286
12.3.2 Linear-Time Selection 294
12.4 Presorting 298
13 Epilogue 304
Answers to Exercises 307
Appendix: Notation and Standard Results from Probability Theory 367
A. 1 Logarithms 367
A.2 Asymptotics 367
A.3 Harmonic Numbers 368
A.4 Probability 368
Bibliography 373
Index 389
|
| adam_txt |
Contents
Preface xi
Acknowledgments xv
1 Sorting and Associated Concepts 1
1.1 Sorting 1
1.2 Selection 2
1.3 Jargon 4
1.4 Algorithmic Conventions 6
1.5 Order 7
1.6 Binary Trees 10
1.7 Decision Trees 18
1.8 Bounds on Sorting 21
1.8.1 Lower Bounds on Sorting 22
1.8.2 Upper Bounds on Sorting 24
1.9 Bounds on Selection 25
1.9.1 Lower Bounds on Selection 26
1.9.2 Upper Bounds on Selection 33
1.10 Random Permutations 36
1.10.1 Records 41
1.10.2 Inversions 44
1.10.3 Cycles 46
1.10.4 Runs 48
1.11 An Analytic Toolkit 53
1.11.1 The Saddle Point Method 54
1.11.2 The Mellin Transform 56
1.11.3 Poissonization 61
1.11.4 The Dirichlet Transform 67
1.11.5 Rice's Method 74
2 Insertion Sort 83
2.1 A General Framework 84
2.2 A Sufficient Condition for Normality 87
vii
viii Contents
2.3 Linear Insertion Sort 88
2.4 Binary Insertion Sort 95
3 Shell Sort 103
3.1 The Algorithm 103
3.2 Streamlined Stochastic Analysis 105
3.2.1 The Empirical Distribution Function 106
3.2.2 The Brownian Bridge 106
3.2.3 Using the Stochastic Tools 114
3.3 Other Increment Sequences 122
4 Bubble Sort 129
4.1 The Algorithm 129
4.2 A limit Law for Passes 131
4.3 A Limit Law for Comparisons 136
5 Selection Sort 139
5.1 The Algorithm 139
5.2 Analysis 140
6 Sorting by Counting 144
6.1 COUNT SORT 144
6.2 Sorting by Counting Frequencies 146
7 Quick Sort 148
7.1 The Partitioning Stage 148
7.2 Bookkeeping 151
7.3 Quick Sort Tree 152
7.4 Probabilistic Analysis of QUICK SORT 153
7.5 Quick Selection 166
7.5.1 Hoare'sFIND 167
7.5.2 MULTIPLE QUICK SELECT 177
8 Sample Sort 199
8.1 The Small Sample Algorithm 199
8.2 The Large Sample Algorithm 205
9 Heap Sort 212
9.1 The Heap 212
9.2 Sorting via a Heap 217
Contents ix
10 Merge Sort 220
10.1 Merging Sorted Lists 220
10.1.1 LINEAR MERGE 222
10.1.2 BINARY MERGE 227
10.1.3 The HWANG-LIN Merging Algorithm 228
10.2 The Merge Sort Algorithm 230
10.3 Distributions 239
10.4 Bottom-Up Merge Sort 243
11 Bucket Sorts 250
11.1 The Principle of Bucket Sorting 250
11.1.1 Distributive Sorts 253
11.1.2 Radix Sorting 259
11.2 Bucket Selection 269
11.2.1 Distributive Selection 271
11.2.2 Radix Selection 276
12 Sorting Nonrandom Data 283
12.1 Measures of Presortedness 284
12.2 Data Randomization 284
12.3 Guaranteed Performance 286
12.3.1 The FORD-JOHNSON Algorithm 286
12.3.2 Linear-Time Selection 294
12.4 Presorting 298
13 Epilogue 304
Answers to Exercises 307
Appendix: Notation and Standard Results from Probability Theory 367
A. 1 Logarithms 367
A.2 Asymptotics 367
A.3 Harmonic Numbers 368
A.4 Probability 368
Bibliography 373
Index 389 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:33:14Z |
| indexdate | 2024-07-09T21:23:50Z |
| institution | BVB |
| isbn | 0471327107 |
| language | English |
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| physical | XIII, 394 S. graph. Darst. |
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| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Wiley [u.a.] |
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| series2 | Wiley-interscience series in discrete mathematics and optimization |
| spelling | Mahmoud, Hosam M. 1954- Verfasser (DE-588)133633160 aut Sorting a distribution theory Hosam M. Mahmoud New York [u.a.] Wiley [u.a.] 2000 XIII, 394 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-interscience series in discrete mathematics and optimization Literaturverz. S. 373 - 387 Distribution (Probability theory) Sortierverfahren (DE-588)4193434-9 gnd rswk-swf Sortierverfahren (DE-588)4193434-9 s DE-604 http://www.loc.gov/catdir/description/wiley039/99086783.html Publisher description http://www.loc.gov/catdir/toc/onix05/99086783.html Table of Contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016842972&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mahmoud, Hosam M. 1954- Sorting a distribution theory Distribution (Probability theory) Sortierverfahren (DE-588)4193434-9 gnd |
| subject_GND | (DE-588)4193434-9 |
| title | Sorting a distribution theory |
| title_auth | Sorting a distribution theory |
| title_exact_search | Sorting a distribution theory |
| title_exact_search_txtP | Sorting a distribution theory |
| title_full | Sorting a distribution theory Hosam M. Mahmoud |
| title_fullStr | Sorting a distribution theory Hosam M. Mahmoud |
| title_full_unstemmed | Sorting a distribution theory Hosam M. Mahmoud |
| title_short | Sorting |
| title_sort | sorting a distribution theory |
| title_sub | a distribution theory |
| topic | Distribution (Probability theory) Sortierverfahren (DE-588)4193434-9 gnd |
| topic_facet | Distribution (Probability theory) Sortierverfahren |
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