## 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

Exercises

Ex1:

Ex2:

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)

1. 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
2. Mar  15:
The simplex method
Initialization of the simplex method
The dual
3. Mar  22:
The dual
Complementary slackness
Economic interpretation
Feasible vs. Optimal solutions
Farkas Lemma
The minimax theorem
4. Apr 5:
The Ellipsoid algorithm (Yamanitsky-Levin 1982 variant)
5. Apr 12:
The Ellipsoid algorithm with oracle
Theorem D
Bi-stochastic matrices
2-approximation for weighted vertex cover
6. Apr 19:
Approximations for MAX-SAT (randomized and deterministic algorithms)
De-randomization
Approximations for Routing
7. Apr 26:
Approximations for Routing
Approximations for Machine Scheduling (identical+related machines)
Online Algorithms
8. May 3:
Reduction from optimality to feasibility (non-polynomial number of constraints)
Approximations for Machine Scheduling (restricted+unrelated machines)
9. May 10:
Distributed coloring of a circle (upper bound)
Distributed coloring of a circle (lower bound)
10. May 24:
Local ratio - vertex cover
Local ratio - Interval scheduling
11. May 31:
Interval scheduling
Steiner tree
Generalized Steiner forest
12. Jun 7:
Generalized Steiner forest
PTAS for scheduling
13. Jun 14:
PTAS for scheduling
Exercises