CS 420/520: Graph theory with applications to computer science
Amir Nayyeri (Office hours: Thr 3:30pm-4:30pm at KEC 3061)
Pingan Zhu (Office hours: Mon 2:00pm-3:00pm at Kelley Atrium)
Lectures: Tue, Thr 2:00pm-3:20pm in COVL 221
Course description: The course covers efficeient (exact or approximation) algorithms for fundamental graph optimization problems such as minimum spanning trees, shortest paths, maximum matching, planar separators, Steiner trees and traveling salesmans problem.
Tentative topic list:
- Minimum spanning trees, the Brouvka algorithm, the Karger-Klein-Tarjan randomized algorithm
- Shortes paths, the Bellman-Ford algorithm, Goldberg's algorithm
- Maximum matching in bipartite graphs, the Hopkroft-Karp algorithm for bipartite graphs, the randomized algorithm of Goel, Kapralov and Khanna for regular bipartite graphs.
- Random walks, Markov chains, Random walks relation to electrical circuits
- Approximation algorithms, constant factor approximations for the Steiner tree problem, the traveling salesman problem and the multiway cut problem.
- Planar graphs, a quadratice algorithm for planarity testing, the Euler formula, the planar separator theorem and its applications, nessted dissection.
Course requirement: There will be four problem sets.
Prerequisites: (CS 325 or CS 325H) and MTH 232