V22.0310-001

Basic Algorithms, spring 2008

Alan Siegel
MTW, 11-12:15, Room 102

The Tuesday session is for recitation, but a few of these classes will be used for lecture toward the end of the semester.
Office Hours: T,W 12:15-1:15
Teaching Assistance:
TBA


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.

Because of the emphasis on problem solving, students are expected to attend the Tuesday recitation sessions, where sophisticated concepts will be reviewed and illustrated in depth.

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

Required Text:

An Inside Guide to Algorithms: their application, adaptation, design and analysis, by A.R. Siegel and R.J. Cole. Available at Unique Copy Center, 252 Greene St.

Schedule of Topics