On-line and
Approximation Algorithms - 0368.4041
EXAM is on July 1,
2024
This
page will be modified during the course, and will outline the classes.
Grade:
30% exercises
70% exam
Exercises:
Exercise1 (Due on Apr 14, 2024)
Exercise2 (Due on May xx, 2024)
Exercise3 (Due on Jun xx, 2024)
Lecture notes
Text
books:
(1)
Online computation and Competitive Analysis, A Borodin
and R. El-Yaniv, Cambridge university press, 1998.
(2) Approximation Algorithms for NP-hard problems, edited by S. Hochbaum, PWS Publishing company,
1997.
(3) Online Algorithms - The State of the Art, edited by A. Fiat
and G. Woeginger, Springer, 1998.
(4) Papers published in the last 25 years.
(5) Lecture notes from Brics 96 Susanne
Albers
Course syllabus:
Online
algorithms (algorithms that do not have all the information/input in advance)
and some corresponding approximation algorithms.
Course outline
1.
Mar 2022:
Introduction
Examples of approximations algorithms
2 approximation for vertex cover
Examples of on-line problems
Competitive ratio
Ski rental problem - 2 upper/lower bounds
Path searching problem - 9 upper/lower bounds
Machines Scheduling - 2 competitive
2.
Mar 2022:
List update - definitions
List update - various algorithms
List update -2 competitive MF algorithm
List update - 2 lower bound
3.
Mar 2022:
Paging - k competitive LRU/FIFO
Paging - k lower bound
k-server - k general lower bound
k-server on the line - k competitive Double Cover algorithm
4.
Apr 2022:
Randomized algorithms
Quick sort, primality test, max cut
Ski rental - randomized upper/lower bounds
Survival game
Paging - 2H(k) competitive randomized marking algorithm
5.
Apr 2022:
Paging - H(k) randomized lower bound
Oblivious, adaptive on-line and off-line adversaries
Relation between the adversaries
Load balancing - identical machines
6.
Apr 2022:
Load balancing - related machines
Load balancing - restricted assignment - deterministic and randomized lower
bound
7.
Apr 2022:
Load balancing - restricted assignment - upper bound
Load balancing - unrelated machines
Virtual circuit routing
8.
May 2022:
Benefit problems - financial problems - upper/lower bounds
Admission control and routing - general graphs
9.
May 2022:
Admission control and routing - general graphs
Admission control on the line - lower bounds
Admission control on the line - classify & randomly select
10. May 2022:
Admission control on the line - preemptive algorithms
eight variants of admission control on the line:
Deterministic vs. randomized
Non-preemptive vs. preemptive
11. May 2022:
Value =1 vs. value = length
Scheduling problems - maximum completion time identical machines
Scheduling problems - reduction to batch
Response time (flow time) no release times - SPT
12. Jun 2022:
Response time (flow time) with release times - SRPT
EDF for unit size unit value jobs
EDF for jobs of different size
Max value first for unit size jobs with arbitrary value
13. Jun 2022:
Picking the winner
Exercises
Last updated Aug 14,
2023