Algorithmic Methods
- 0368.4139
Yossi Azar (
azar@tau.ac.il )
2nd Semester, 2022/23 - Time: Mon 4-7pm
School of Computer Science,
Tel-Aviv University
For the outline of the course given in 2021 see course2021
Previous Exams
Exercises
Ex1: ex1
Ex2: ex2
Ex3: ex3
Grade:
30%
exercises
70% exam (on July 24, 2023 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
1. Mar
13:
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 20:
The simplex method
Initialization of the simplex method
The dual
3. Mar 27:
The dual
Complementary slackness
Economic interpretation
Feasible vs. Optimal solutions
Farkas Lemma
The minimax theorem
4. Apr
17:
The Ellipsoid algorithm (Yamanitsky-Levin 1982
variant)
5. Apr
24:
The Ellipsoid algorithm with oracle
Theorem D
Bi-stochastic matrices
2-approximation for weighted vertex cover
6. May
1:
Approximations for MAX-SAT (randomized and deterministic algorithms)
De-randomization
Approximations for Routing
7. May
8:
Approximations for Routing
Approximations for Machine Scheduling (identical + related machines)
Online Algorithms
8. May
15:
Reduction from optimality to feasibility (non-polynomial number of constraints)
Approximations for Machine Scheduling (restricted + unrelated machines)
9. May
22:
Distributed coloring of a circle (upper bound)
Distributed coloring of a circle (lower bound)
10. May
29:
Local ratio - vertex cover
Local ratio - Interval scheduling
11. Jun
5:
Interval scheduling
Steiner tree
Generalized Steiner forest
12. Jun
12:
Generalized Steiner forest
PTAS for scheduling
13. Jun
19:
PTAS for scheduling
Exercises
14. Jun
26: extra
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