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

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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:

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)

  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

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 Jan 26, 2021