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CPS 230
DESIGN AND ANALYSIS
OF ALGORITHMS
Fall 2008
Instructor:Herbert Edelsbrunner
Teaching Assistant:Zhiqiang Gu
CPS 230Fall Semester of 2008
Table of Contents
1 Introduction 3
I DESIGNTECHNIQUES4
2 Divide-and-Conquer 5
3 Prune-and-Search 8
4 Dynamic Programming 11
5 Greedy Algorithms 14
First Homework Assignment 17
II SEARCHING18
6 Binary Search Trees 19
7 Red-Black Trees 22
8 Amortized Analysis 26
9 Splay Trees 29
Second Homework Assignment 33
III PRIORITIZING34
10 Heaps and Heapsort 35
11 Fibonacci Heaps 38
12 Solving Recurrence Relations 41
Third Homework Assignment 44IV GRAPHALGORITHMS45
13 Graph Search 46
14 Shortest Paths 50
15 Minimum Spanning Trees 53
16 Union-Find 56
Fourth Homework Assignment 60
V TOPOLOGICALALGORITHMS61
17 Geometric Graphs 62
18 Surfaces 65
19 Homology 68
Fifth Homework Assignment 72
VI GEOMETRICALGORITHMS73
20 Plane-Sweep 74
21 Delaunay Triangulations 77
22 Alpha Shapes 81
Sixth Homework Assignment 84
VII NP-COMPLETENESS85
23 Easy and Hard Problems 86
24 NP-Complete Problems 89
25 Approximation Algorithms 92
Seventh Homework Assignment 95
21 IntroductionMeetings.We meet twice a week, on Tuesdays and
Thursdays, from 1:15 to 2:30pm, in room D106 LSRC. Communication.The course material will be delivered in the two weekly lectures. A written record of the lec- tures will be available on the web, usually a day after the lecture. The web also contains other information, such as homework assignments, solutions, useful links, etc. The main supporting text is TARJAN.Data Structures and Network Algorithms.SIAM, 1983.The book focuses on fundamental data structures and graph algorithms, and additional topics covered in the course can be found in the lecture notes or other texts in algorithms such as
KLEINBERG ANDTARDOS.Algorithm Design.Pearson Ed-
ucation, 2006. Examinations.There will be a final exam (covering the material of the entire semester) and a midterm (at the be- ginning of October), You may want to freshen up your math skills before going into this course. The weighting of exams and homework used to determine your grades is homework 35%, midterm 25%, final 40%.Homework.We have seven homeworks scheduled
throughout this semester, one per main topic covered in the course. The solutions to each homework are due one and a half weeks after the assignment. More precisely, they are due at the beginning of the third lecture after the assignment. The seventhhomeworkmay help you prepare for the final exam and solutions will not be collected.Rule 1. Thesolutionto anyone homeworkquestionmust
fit on a singlepage(togetherwith the statementofthe problem). Rule 2. The discussion of questions and solutions before the due date is not discouraged, but you must formu- late your own solution. Rule 3. The deadline for turning in solutions is 10 min-utes afterthe beginningof the lecture onthe due date.Overview.The main topics to be covered in this course
are