Algorithmic Methods - 0368.4139

Yossi Azar ( azar@tau.ac.il )
1st Semester, 2018/9 - Time: Mon 4-7pm
School of Computer Science,
Tel-Aviv University

This page will be modified during the course, and will outline the classes.
For the outline of the course given in 2016 see course2016

New (Previous Exams)

Exam 2016/7

Exam 2014/5

Exam 2012/3

Exam 2010/1

Exercises

Ex1: ex1

Ex2: ex2

Ex3: ex3

Grade:

30% exercises
70% exam (on January 21^st, 2019 at 9:00am)

Text books (only couple of chapters from each book)

(1) Linear Programming by H. Karloff, Birkhauser, 1991.
(2) Introduction to Algorithms by T. Cormen, C. Leiserson and R. Rivest, MIT Press, 1990
(3) Approximation Algorithms for NP-hard problems edited by S. Hochbaum, PWS Publishing company, 1997.
(4) Approximation Algorithms by Vijay Vazirani, Springer, 2003.
(5) Survey on Local Ratio Survey

Course syllabus:

Linear Programming - simplex, duality, the ellipsoid algorithm, applications.
Approximation algorithms,

Randomized algorithms, De-randomization,

Distributed and Parallel algorithms,
On-line algorithms.

Course outline (will be updated during the course)

1. Oct 15:
   Introduction
   Examples of linear programming problems
   Basic definitions (canonical, standard, general forms, polyhedron, polytope, basic feasible solution)
   Theorems A, B, C on polyhedrons and their vertices
2. Oct 22:
   The simplex method
   Initialization of the simplex method
   The dual
3. Oct 29:
   The dual
   Complementary slackness
   Economic interpretation
   Feasible vs. Optimal solutions
   Farkas Lemma
   The minimax theorem
4. Nov 5:
   The Ellipsoid algorithm (Yamanitsky-Levin 1982 variant)
5. Nov 12:
   The Ellipsoid algorithm with oracle
   Theorem D
   Bi-stochastic matrices
   2-approximation for weighted vertex cover
6. Nov 19:
   Approximations for MAX-SAT (randomized and deterministic algorithms)
   De-randomization
   Approximations for Routing
7. Nov 26:
   Approximations for Routing
   Approximations for Machine Scheduling (identical+related machines)
   Online Algorithms
8. Dec 3:
   Reduction from optimality to feasibility (non-polynomial number of constraints)
   Approximations for Machine Scheduling (restricted+unrelated machines)
9. Dec 10:
   Distributed coloring of a circle (upper bound)
   Distributed coloring of a circle (lower bound)
10. Dec 17:
    Local ratio - vertex cover
    Local ratio - Interval scheduling
11. Dec 24:
    Interval scheduling
    Steiner tree
    Generalized Steiner forest
12. Dec 31:
    Generalized Steiner forest
    PTAS for scheduling
13. Jan 7:
    PTAS for scheduling
    Exercises

Lecture notes template

noteTemplate.tex
noteTemplate.pdf

Lecture notes

Class-1 on 18.10.2010
Class-2 on 25.10.2010
Class-3 on 1.11.2010
Class-4 on 8.11.2010
Class-5 on 15.11.2010
Class-6 on 22.11.2010
Class-7 on 29.11.2010
Class-8 on 6.12.2010
Class-9 on 13.12.2010
Class-10 on 20.12.2010
Class-11 on 27.12.2010
Class-12 on 3.1.2011
Class-13 on 10.1.2011

Last updated Sep 17, 2018