Fundamental Algorithms

Alan Siegel

Lecture: M 5:10-7:00, Room 102

Recitation: Th 5:10-6:00, Room 109

Please note that the recitation is in a different room
Office Hours: Th 6-7, Th 2-3 and by appointment
Phone: 998-3122



This course covers the design and analysis of combinatorial algorithms. The curriculum is concept-based and emphasizes the art of problem-solving. The class features weekly exercises designed to strengthen conceptual understanding and problem solving skills. Students are presumed to have adequate programming skills and to have a solid understanding of basic data structures and their implementation in the programming languages of their choice. Although some mathematical sophistication is very helpful for this course, the necessary mathematics is contained within the curriculum.

In some recitation sessions, sophisticated problems will be solved by the class in closely supervised individual, collaborative, and group efforts. Other recitation sessions will be used for additional lecture.

Required Text:

An Introduction to Algorithms: their Methods and ssendaM, by A.R. Siegel.
A new edition of the text will be used for this course, and will be available before the first day of class.
The details for acquiring the text will be posted here as soon as it becomes available.

Course Topics

Algorithmic Design Paradigms

Recursion
Depth-First-Search
Breadth-First-Search
The Greedy Method
Divide-and-Conquer
Dynamic Programming
Sorting- and Selection-based processing
Randomization
Algorithm Redesign and Adaptation
Problem Transformations

The Analysis of Algorithmic Performance

Asymptotic Growth
Recurrence Equations
The Recursion Tree Solution Method
Probabilistic Analysis
Structural Analysis
Lower Bounds

Managing Data for Efficient Processing

Lists, Stacks, Queues, Priority Queues, Trees and Graphs
Tarjan's Categorization of Data Structures
Search Trees and their Enhancement
Union-Find
Sorting, Selection, and Hashing

Selected Representative Algorithms/problems

Topological Sort
Connected Components
Biconnected Components and Strong Components
Representative styles of Dynamic Programming and their applications
Standard Sorting and Selection Algorithms
Selected topics in Hashing
Minimum Spanning Trees
Shortest Path Problems

An approximate schedule of topics can be found here.

It will change as the lectures and organization are adapted to fit the current time constraints.

Homework

Course Grading Policy