On-line Algorithm Homework2
Presenter: W. Choi
Problem: Exercise 10.4
Problem Description:
Prove the following 2-server algorithm ALG is O(1)-competitive in
any Euclidean Space.
ALG: After serving each request, label the server at the request s1 and the
A
Exercise 2.4 Consider the following generalization of RMTF. For any real
p [0,1] , let RMTFp be the algorithm that, upon a request for an item x,
moves x to the front with probability p. Generalize the lower bound to
RMTFp for each p (0, )] .
Algorithm RM
Spring Semester 2004
2004/02/21
CSE 5314 On-line Computation
Homework Set 01
File: HW01PPL
Homework Set 1
Exercise 1.2
Page 6
Online Computation And
Competitive Analysis
Borodin & El-Yaniv
CSE@UTA
CSE 5314 On-line Computation
Copyright by H. J. Kearny. Al
Exercise 3.3 Show that LRU does not incur Beladys anomaly but that
FIFO does incur the anomaly
Beladys Anomaly: Some reference strings generate more page faults when
more page frames are allotted.
1) FIFO (First-In/First-Out): Replace the page that has be
Homework 1
CSE 5314
Rui Huang
2/18/2004
Exercise 1.8 Let L be a list of two elements x and y. Prove that there is an optimal
offline algorithm OPT for L that satisfies the following properties: 1) OPT does not use
paid exchanges; and 2) whenever there is
Spring Semester 2004
2004/02/21
CSE 5314 On-line Computation
Homework Set 01
File: HW01PPL
Homework Set 1
Exercise 3.5
Page 38
Online Computation And
Competitive Analysis
Borodin & El-Yaniv
CSE@UTA
CSE 5314 On-line Computation
Copyright by H. J. Kearny. A
Spring Semester 2004
2004/02/21
CSE 5314 On-line Computation
Homework Set 01
File: HW01PPL
Homework Set 1
Exercise 4.5
Page 50
Online Computation And
Competitive Analysis
Borodin & El-Yaniv
CSE@UTA
CSE 5314 On-line Computation
Copyright by H. J. Kearny. A
Correctness of Work Function Algorithm for Metrical Task Systems
Usual dynamic programming table is constructed, but WFA selects one entry wi+1( si+1) in each row.
This is a state j that minimizes wi+1( j ) + d(si , j) where si is the WFA choice in previo
Exercise 1.7 (page 11)
For the static list accessing problem with l
items,
Instead of using a bound on the average
(over all initial configurations) static
optimal to derive 2l/(l+1) lower bound,
show that we can use the frequency count
of items in the
Three Structurally Similar List Update Upper Bound Proofs
Review of amortized complexity:
ci = ci + (i) (i 1)
ci = ci + (i 1) + (i)
n
n
ci = ci + (0) ( n )
i=1
i=1
n
n
If (0) ( n ) is never positive, then an upper bound on ci is an upper bound on ci .
i=
CSE 5314 Lab Assignment 2
Due April 29, 2004
Goal:
Understanding of the work function algorithm for the k-server problem.
Requirements:
1.
Extend your dynamic programming solution to lab 1 to implement the work function algorithm.
2.
Provide hardcopy list
CSE 5314 Homework Set 1
Presentations Tentatively February 24 & 26
Reservations at http:/reptar.uta.edu/NOTES5314/hw1.txt
Each student should choose three problems from at least two different chapters.
1.
1.1
21. 3.2
2.
1.2
22. 3.3
3.
1.3
23. 3.4
4.
1.4
2
CSE 5314 Lab Assignment 1
Due March 9, 2004
Goals:
1.
Understanding of the k-server problem.
2.
Understanding of three approaches to the offline solution of the k-server problem: assignment problem (minimum-weight
bipartite matching), dynamic programming,