Algorithm Design, Analysis, and Implementation
Learning Objective:To learn about and be able to apply data structures techniques and algorithm design and analysis techniques as the graduate level. To understand and construct lower bound proofs, as well as prove membership in problem classes such as NP-complete and PSPACE-complete.
Description:Basic techniques for designing and analyzing algorithms: dynamic programming, divide and conquer, balancing. Upper and lower bounds on time and space costs, worst case and expected cost measures. A selection of applications such as disjoint set union/find, graph algorithms, search trees, pattern matching. The polynomial complexity classes P, NP, and co-NP; intractable problems.
Topics Covered:Recurrence Relations
Prune and Search, and Divide and Conquer
Data Structures including Fibonacci heaps, disjoint sets
Graph Algorithms including max flow (Goldberg-Tarjan)
Lower Bound Techniques
NP-complete Problems including approximation algorithms
Prerequisites:A bachelor degree in computer science or an equivalent field. Students not in the Computer Science master's program should seek department permission to register.
An undergraduate course in the analysis of algorithms, and an undergraduate course in the discrete mathematics used in computer science.