CME 305: Discrete Mathematics and Algorithms
Instructor: Reza Zadeh
Time: Tue, Thu 1:30 PM - 2:50 PM
Room: Econ 140
- Basic Algebraic Graph Theory
- Minimum Spanning Trees and Matroids
- Maximum Flow and Submodularity
- Approximation Algorithms
- Randomized Algorithms
- The Probabilistic Method
- Spectral Sparsification
This course is targeting doctorate students with strong foundations in mathematics who wish to become more familiar with the design and analysis of discrete algorithms. An undergraduate course in algorithms is not a prerequisite, only familiarity with basic notions in linear algebra and discrete mathematics.
Grade breakdown: 50% final, 30% midterm, 20% assignments (4 of them). The midterm and final will be good practice for the ICME qualifying exam.
Algorithm Design by Kleinberg and Tardos [KT]
Graph Theory by Reinhard Diestel [D]
Approximation Algorithms by Vijay Vazirani [V]
Randomized Algorithms by Rajeev Motwani and Prabakhar Raghavan [MR]
The Probabilistic Method by Noga Alon and Joel Spencer [AS]
Midterm: Thursday, Feb 11th
- Assignment 1, [pdf] [tex], Due at the beginning of class Thursday 01/21 Solutions.
- Assignment 2, [pdf] [tex], Due at the beginning of class Thursday 02/04 Solutions.
Note that these references are not intended to be any substitute for the material covered during lectures.
- Tu 1/5: Lecture 1 (Intro to Graph Theory, Karger's Global Min-Cut): D 1.1-1.6; Notes; A New Approach to the Minimum Cut Problem (Karger and Stein)
- Th 1/7: Lecture 2 (s-t Min-Cut, Max-Flow, Ford-Fulkerson): KT 7: Notes
- Tu 1/12: Lecture 3 (Applications of Max-Flow, Probabilistic Method): Notes; MR 5; AS 1
- Th 1/14: Lecture 4 (Minimum Spanning Trees, Exhausting a Graph): Notes
- Tu 1/19: Lecture 5 (Randomized Walks and Electrical Networks): Notes 1; Notes 2; MR 6
- Th 1/21: Lecture 6 (Markov Inequality; Tighter Bounds for Cover Times): Notes
- Tu 1/26: Lecture 7 (Problem Classes, Reductions): Notes; The NP Compendium; KT 8
- Th 1/28: Lecture 8 (Approximation Algorithms): Notes; KT 11
- Tu 2/3: Lecture 9 (TSP; Dynamic Programing): KT 6
- Th 2/5: Lecture 10 (Dynamic Programming, Cover Times): KT 6
- Tu 2/9: Lecture 11 (Midterm Review): Problem session 1 and 2
- Th 2/11: Lecture 12 (Midterm)
Spring 2012 Qual pdf.
Fall 2012 Qual pdf.
Spring 2013 Qual pdf.
2015 Midterm pdf, Solutions pdf
2014 Midterm and Solutions pdf,
2011 Midterm pdf,
2010 Midterm pdf,
Practice Midterm 1 (In-Class) pdf,
Practice Midterm 2 (In-Class) pdf,
Problem Session 2/11/15 and Solutions
Problem Session 2/10/15 and Solutions
Problem Session 2/10/14 and Solutions
Problem Session 2/20/14 and Solutions
Winter 2015: Class website
Winter 2014: Class website
Reza Zadeh (rezab at stanford)
Office hours: by appointment
Arun Jambulapati (jmblpati at stanford)
Office hours: 3-5pm on Tuesdays
Qingyun Wu (wqy at stanford)
Office hours: 3-5pm on Wednesdays
TA office hours will be held in the Huang Engineering Center basement (in front of the ICME office)