Algorithmic Methods
- 0368.4139
Yossi Azar (
azar@tau.ac.il )
2nd Semester, 2020/21 - 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 2018 see course2018
Previous Exams
Exercises
Ex1: ex1
Ex2: ex2
Ex3: ex3
Grade:
30%
exercises
70% exam (on July 1st, 2021 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)
- Mar 8:
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 - Mar 15:
The simplex method
Initialization of the simplex method
The dual - Mar 22:
The dual
Complementary slackness
Economic interpretation
Feasible vs. Optimal solutions
Farkas Lemma
The minimax theorem - Apr 5:
The Ellipsoid algorithm (Yamanitsky-Levin 1982 variant) - Apr 12:
The Ellipsoid algorithm with oracle
Theorem D
Bi-stochastic matrices
2-approximation for weighted vertex cover - Apr 19:
Approximations for MAX-SAT (randomized and deterministic algorithms)
De-randomization
Approximations for Routing - Apr 26:
Approximations for Routing
Approximations for Machine Scheduling (identical+related machines)
Online Algorithms - May 3:
Reduction from optimality to feasibility (non-polynomial number of constraints)
Approximations for Machine Scheduling (restricted+unrelated machines) - May 10:
Distributed coloring of a circle (upper bound)
Distributed coloring of a circle (lower bound) - May 24:
Local ratio - vertex cover
Local ratio - Interval scheduling - May 31:
Interval scheduling
Steiner tree
Generalized Steiner forest - Jun 7:
Generalized Steiner forest
PTAS for scheduling - Jun 14:
PTAS for scheduling
Exercises
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