Algorithm, complexity, analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Greifswald
Academica Greifswald
2012
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 317 S. graph. Darst. |
| ISBN: | 9783940237286 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV040340509 | ||
| 003 | DE-604 | ||
| 005 | 20120807 | ||
| 007 | t | ||
| 008 | 120730s2012 d||| |||| 00||| eng d | ||
| 020 | |a 9783940237286 |9 978-3-940237-28-6 | ||
| 035 | |a (OCoLC)812199751 | ||
| 035 | |a (DE-599)BVBBV040340509 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 | ||
| 084 | |a ST 134 |0 (DE-625)143590: |2 rvk | ||
| 100 | 1 | |a Burdescu, Dumitru Dan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algorithm, complexity, analysis |c Dumitru Dan Burdescu ; Marian Cristian Mihăescu |
| 264 | 1 | |a Greifswald |b Academica Greifswald |c 2012 | |
| 300 | |a 317 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Mihăescu, Marian Cristian |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025194785&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025194785 | ||
Datensatz im Suchindex
| _version_ | 1804149373613899776 |
|---|---|
| adam_text | CONTENTS
Preface
.................................................................................................................5
Chapter
1
Introduction to Algorithms Complexity Analysis...
........................................7
1.
Mathematical Functions Used in the Algorithms Analysis
........................7
1.1.
The Constant Function
........................................................................7
1.2.
The Logarithm Function
.....................................................................7
1.3.
The Linear Function
..................................................................,.........9
1.4.
The NlogN Function.....
.....................................................................10
1.5.
The Quadratic Function
.............,......................................................10
1.6.
The Cubic Function and Other Polynomials
.....................................
1
1
1.6.1.
Polynomials
...............................................................................12
1.6.2.
Summations
..........................................,....................................13
1.7.
The Exponential Function...
..............................................................13
1.7.1.
Geometric Sums
....................................................................... 14
2.
Performing Experimental Studies
.............................................................15
2.1.
Computing Running Times
...............................................................15
2.2.
Primitive Operations
..................,......................................................16
3.
Asymptotic Notation and Analysis
..........................................................18
4.
Complexity Classes..
.................................................................................21
4.1.
Introduction to Turing Machines
,.....................................................21
4.2.
Ρ
Class -Problems Solvable in Polynomial Time.,
..........................24
4.3.
NP Class
-
Problems Solvable by Nondetermmistic Polynomial
Time.....
.............................................................................................27
4,3.1.
NP-Complete Problems
.............................................................28
5.
Assignments
..............................................................................................29
Chapter
2
Time and Space Complexity
...........................................................................30
1.
Theoretical Aspects....
....................................................................................30
Chapters
Binomial Heaps and Fibonacci Heaps
............................................................47
1.
Binomial Heaps
.........................................................................................47
1.1.
Binomial Trees
..................................................................................47
312
1.2.
Representation of
Binomial
Heaps
...................................................50
1.3.
Operations on Binomial Heaps
.........................................................51
1.3.1.
Creating a New Binomial Heap.,
..............................................51
1.3.2.
Finding the Minimum Key
.......................................................51
1.3.3.
Uniting Two Binomial Heaps
...................................................52
1.3.4.
Inserting a Node in a Binomial Heap
........................................54
1.3.5.
Extracting the Node with Minimum Key
..................................55
1.3.6.
Decreasing a Key
......................................................................56
1.3.7.
Deleting a Key
.......................................................................... 57
2.
Fibonacci Heaps
........................................................................................58
2.1.
The Structure of Fibonacci Heaps
......................................................58
2.2.
Inserting a Node into a Fibonacci Heap.....
..........,............................59
2.3.
Uniting Two Fibonacci heaps
...........................................................61
2.4.
Deleting the Minimum Node
........................................................... 62
2.5.
Decreasing a Key
.,..........,................................................................. 65
2.6.
Deleting a Node
................................................................................66
3.
Assignments
..............................................................................................67
4.
Sample Implementations.....
.....................................................................68
4.1.
Sample implementation of Binomial Heaps
.....................................68
4.2.
Sample implementation of Fibonacci Heaps
....................................73
Chapter
4
M
and M+Trees,
............................................................................................,.84
1.
Introduction to Metric Space Searching
....................................................84
1.1.
The Metric Space
.............................................................................84
1.1.1.
Distances Measures.
.................................................................,84
1.1.1.1.
Euclidian Distance
............................................................85
1.1.1.2.
Minkowski Distances......
..................................................85
1.1.1.3.
Edit Distances.
..................................................................86
1.1.1.4.
Tree Edit Distances
...........................................................86
1.1.1.5.
Time Complexity
..............................................................86
1.2.
Fundamental Concepts of Metric Space Searching
..........................87
1.2.1.
Similarity Queries
....................................................................,87
1.2.1.1.
Range Queries
..................................................................87
1.2.1.2.
Nearest Neighbor Queries
.................................................88
1.2.2.
Basic Partitioning Principles,....
................................................89
1.2.2.1.
Ball Partitioning
...............................................................89
1.2.2.2.
Generalized
Hyperplane
Partitioning.................
...............90
1.2.2.3.
Clustering
..........................................................................91
2.
M
Trees
.....................................................................................................91
2.1.
Operations on
M
Trees..................
....................................................93
2.1.1.
Building an
M
Tree
....................................,..,.,.........................93
2.1.2.
Range Queries in
M
Tree
..........................................................95
313
2.1.3.
к
Nearest Neighbors Queries in
M
Tree
..................................96
2.2.
Sample Building of an
M
Tree structure
........................,..................98
3.M+Trees
.................................................................................................101
3.1.
The Structure of M+ Nodes
............................................................103
3.2.
Building an M+ Tree
.......................................................................104
3.3.
Range Queries in M+ Tree
..............................................................105
3.4.
к
Nearest Neighbors Queries
inM+
Tree
.......................................106
3.5.
Sample Building of an M+ Tree structure
......................................108
4.
Assignments
............................................................................................
Ill
5.
Sample Implementations
........................................................................112
5.1.
Implementation of
M
Trees
............................................................112
5.2.
Implementation of M+ Trees
..........................................................117
Chapter
S
R,
R+,
R*
Trees
..............................................................................................123
1.
RTrees
...................................................................................................123
1.1.
The Structure of R-Tree
..................................................................123
1.2.
Search Operation in R-Tree
............................................................125
1.3.
Insert Operation in R-Tree
..........................................,..................125
1.4.
Deletion Operation in R-Tree
,........................................................ 127
1.5.
Node Splitting Policies...
................................................................. 128
1.5.1.
Exhaustive Algorithm
.............................................................129
1.5.2.
A Quadratic-Cost Algorithm.
.................................................129
1.5.3.
A Linear-Cost Algorithm
.............,.......................................... 130
Î.6.
Sample Building of an
R
Tree Structure
......................................... 131
2.
R+Trees.........
.........................................................................................134
2.Ì.
The Structure of R-f-Tree
................................................................ 138
2.2.
Search Operation in
Rł-Tree
......................,......................,............ 138
2.3.
Insertion Operation in
R+-Tree
........,.............................................. 139
2.4.
Deletion Operation in R+^ree
...................................................... 139
2.5.
Node Splitting Operation in
Rł-Tree
............................................140
2.6.
Packing Algorithm
............................................«..................,.......... 142
2.7.
Sample Building of an
R
-ь
Tree Structure
.......................................144
3.R* Trees
..................................................................................................150
3.1.
The Algorithm ChooseSubtree..
.......................................................151
3.2.
Split of the R* Tree
.........................................................................
Î52
3.3.
Forced Reinsert in R* Tree
.............................................................154
4.
Assignments
............................................................................................155
5.
Sample Implementations
.........................................................................156
5.1.
Sample Implementation of
R
Trees
...............................................156
5.2.
Sample Implementation ofR+ Trees
..............................................160
314
Chapter
6
The Maximum Flow Problem..
.....................................................................164
1.
General Presentation
..............................................................................164
2.
Ford-Fulkerson Algorithm
......................................................................166
2.1.
General Presentation
.......................................................................166
2.1.1.
Detailed Running of Ford-Fulkerson Algorithm
....................167
3.
Edmonds-Karp Algorithm
.......................................................................169
3.1.
General Presentation
......................................................................169
3.1.1.
Detailed Running of Edmonds-Kaip Algorithm
.....................170
4.
Dime s Algorithm
...................................................................................172
4.1.
General Considerations
...................................................................172
4.2.
Detailed Running of Dinic s Algorithm
..........................................174
5.
Push-Relabel Algorithm
..........................................................................177
5.1.
General Considerations
..................................................................177
5.1.1.
Intuitive Approach Towards the Algorithm
...........................177
5.1.2.
Definitions
...............................................................................177
5.1.3.
Operations..
.............................................................................178
6.
Assignments
............................................................................................183
7.
Sample Implementations
........................................................................184
7.1.
Sample Implementation of Maximum Flow Problem Using
Ford-Fulkerson Algorithm
..............................................................184
7.2.
Sample Implementation of Maximum Flow Problem Using
Edmonds-Karp Algorithm...
............................................................186
Chapter
7
Consistency Problem
Maximum Match in a Bipartite Graph
........................................................188
1.
General Presentation
.............................................................................. 188
2.
The Unger s Algorithm..
.....,................................................................... 189
2.1.
General Presentation
.......................................................................189
2.2.
Sample Running of Unger s Algorithm
........................................., 198
2.2.1.
Example
Î
............................................................................... 198
2.2.2.
Example
2...............................................................................199
3.
Assignments
............................................................................................204
4.
Sample Implementation...
.......................................................................205
Chapter
8
TSP-The Travelling Salesman Problem
.......................................................207
1.
General Presentation
..............,..............................................................„207
2.
Backtracking Approach
...........................................................................209
2.1.
Generai
Presentation......
..........................,......................................209
3.
Greedy Method
......................................................................,................214
3.1.
General Presentation
.........„............................................................214
315
3.1.1.
Detailed Running of Greedy Algorithm
.....,............................215
4.
Heuristic Method...
..................................................................................216
4.1.
General Considerations
...................................................................216
4.2.
Detailed Running of Heuristic Method
...........................................218
5.
Assignments
............................................................................................219
6.
Sample implementations
........................................................................219
6.1.
Backtracking Implementation
.........................................................219
6.2.
Greedy Implementation
...................................................................220
6.3.
Heuristic Implementation
..............................................................„222
Chapter
9
A* Algorithm
..................................................................................................224
1.
General Presentation
..............................................................................224
1.1.
A* Algorithm
..................................................................................227
2.
Detailed Running Of A* Algorithm
.......................................................229
3.
Assignments
............................................................................................228
4.
Sample Implementation
..............................................................,...........238
Chapter
10
Satisfiability and Graph Coloring
................................................................246
1.
General Presentation.....
..........................................................................246
1.1.
Satisfiability
....................................................................................246
1.2.
Graph Coloring Algorithms
............................................................253
1.2.1.
2-Colormg of a Graph..
...........................................................253
1.2.2.
k-Coloring of a Graph
-
Backtracking Approach
...................255
1.2.3.
k-Coloring of a Graph ~ Greedy Approach
............................259
2.
Assignments......
............................................................................,..„.....262
3.
Assignments.........
................................................................................,..262
3.Î.
Backtracking Implementation
................................................,.,.„...262
3.2.
Greedy implementation
..................................................................263
Chapter
11
Decision Trees
......................................,..........................................................269
1.
Theoretical Aspects
.................,................................................,..............269
2.
Sample Usage Of Decision Trees: Game Trees
......................................277
3.
Assignments.........
...........................,.......................................................281
4.
Sample Implementation
..........................................................................282
Chapter
12
Randomized Binary Search Trees
................................................................293
1.
General Presentation
...............................................................................293
1.1.
Randomized Binary Search Trees
...................................................293
1.1.1.
Search Operation in TREAP Structures
.................................,296
316
1.1.2.
Insertion in TREAP Structures
..............................................296
1.1.3.
Delete Operation
in TREAP
Structures
..................................299
1.1.4.
Split Operation in TREAP Structures
.....................................300
1.1.5.
Merge Operation in TREAP Structures
..................................302
2.
Assignments
............................................................................................303
3.
Sample Implementation
.........................................................................304
REFERENCES
...........................................................................................,...310
317
Univ,-
Bibliothek-
Passan
;
|
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| spelling | Burdescu, Dumitru Dan Verfasser aut Algorithm, complexity, analysis Dumitru Dan Burdescu ; Marian Cristian Mihăescu Greifswald Academica Greifswald 2012 317 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mihăescu, Marian Cristian Verfasser aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025194785&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burdescu, Dumitru Dan Mihăescu, Marian Cristian Algorithm, complexity, analysis |
| title | Algorithm, complexity, analysis |
| title_auth | Algorithm, complexity, analysis |
| title_exact_search | Algorithm, complexity, analysis |
| title_full | Algorithm, complexity, analysis Dumitru Dan Burdescu ; Marian Cristian Mihăescu |
| title_fullStr | Algorithm, complexity, analysis Dumitru Dan Burdescu ; Marian Cristian Mihăescu |
| title_full_unstemmed | Algorithm, complexity, analysis Dumitru Dan Burdescu ; Marian Cristian Mihăescu |
| title_short | Algorithm, complexity, analysis |
| title_sort | algorithm complexity analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025194785&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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