15-750
HW 0 Solutions
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 0 Solutions
1
Asymptotic Notation
[10 points] For each list of functions, order them accordi
15-750
HW 6
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 6 Due date: Friday, May 1
Some Reminders:
Read the Policies section on the course web site before you
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 6 Solutions
1
Separators in outer planar graphs (20 pts.)
(a) We say that a graph is outer planar if it is 1) planar
MATHcfw_3/M2510 Optimisation 34
Friday, 30 January, 2009
Lecture 3
Lecturer: Aram W. Harrow Farkas Lemma and strong LP duality
3.1
Using reductions between LPs to extend Farkas Lemma
Yesterday we saw
CSC2411 - Linear Programming and Combinatorial Optimization Lecture 6: LP Duality, Complementary slackness, Farkas Lemma, and von Neumann min-max principle.
Notes taken by Pixing ZHANG February 17, 20
Note 3: LP Duality
If the primal problem (P) in the canonical form is min Z = n=1 cj xj j n i = 1, 2, ., m s.t. j =1 aij xj bi xj 0 j = 1, 2, ., n, then the dual problem (D) in the canonical form is m
Note 5: Duality and Dual Simplex Method
If the primal problem (P) is max Z = n=1 cj xj j n s.t. aij xj bi i = 1, 2, ., m j =1 xj 0 j = 1, 2, ., n, then the dual problem (D) is min W = m bi yi i=1 m s.
15-750
Midterm 2
Page 1 of 9
15-750: Practice Midterm 2
Name: Email:
Instructions Fill in the box above with your name, and your email address. Do it, now! This exam is open book: That is, you may use
15-750
Midterm 2
Page 1 of 9
15-750: Practice Midterm 2
Name: Email:
Instructions Fill in the box above with your name, and your email address. Do it, now! This exam is open book: That is, you may use
15-750-s09
Practice Final
Page 1 of 6
15-750-S09: Practice Final
Name: Email:
Instructions Fill in the box above with your name, and your email address. Do it, now! This exam is open book: That is, yo
15-750
Midterm 1
Page 1 of 9
15-750: Practice Midterm 1
Name: Email:
Instructions Fill in the box above with your name, and your email address. Do it, now! This exam is open book: That is, you may use
Automatic Recording Problem
1
In this programming assignment, you will use linear programming to obtain an upper bound on the objective for the integer automatic recording problem (ARP). Integer ARP i
CS149
Introduction to Combinatorial Optimization
Homework 6
Due: 4:00 pm, Wed, Nov 4th
Problem 1
We want to buy some quantity of meat and bread, in order to satisfy some dietary needs. A kg of meat co
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 5 Solutions
1
Something about Laplacian (25 pts.)
The Laplacian of a graph encodes a number of interesting propertie
15-750
HW 5
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 5 Due date: Wednesday, April 15
Some Reminders:
Read the Policies section on the course web site befo
15 September 2003
Solving Linear and Integer Programs
Robert E. Bixby
ILOG, Inc. and Rice University
Ed Rothberg
ILOG, Inc.
Outline
Linear Programming: Bob Bixby
Example and introduction to basic LP,
CHAPTER VIII
CONVEX SETS
We present some geometric aspects of linear programming. Definition. A subset S of n is said to be convex, if given x and y in S, then the line segment [x,y] connecting x and
Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard
LP Methods.S1 Dual Simplex Algorithm
In the tableau implementation of the primal simplex algorithm, the right-hand-side colum
Farkas Lemma
Rudi Pendavingh
Eindhoven Technical University
Optimization in Rn , lecture 2
Rudi Pendavingh (TUE)
Farkas Lemma
ORN2
1 / 14
Todays Lecture
Theorem (Farkas Lemma, 1894)
Let A be an m n ma
15-750
HW 0
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 0 Due date: January 23
Some Reminders: Read the Policies section on the course web site before you sta
15-750
HW 1
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 1 Due date: Friday, February 6
Some Reminders:
Read the Policies section on the course web site befor
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 1 Solutions
1
Fibonaccimal Numbers (25 pts.)
Suppose instead of using powers of two, we now represent integers as th
15-750
HW 2
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 2 Due date: Friday, February 20
Some Reminders:
Read the Policies section on the course web site befo
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 2 Solutions
1
Traveling Salesman (25 pts.)
In the traveling salesman problem we are given n cities and all distances
15-750
HW 3
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 3 Due date: Wednesday, March 18
Some Reminders:
Read the Policies section on the course web site befo
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 3 Solutions
1
Duality Theory (25 pts.)
Given a linear program mincfw_c x : Ax b, x 0 and a solution x0 , how can one
15-750
HW 4
1
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 4 Due date: Monday, March 30
Some Reminders:
Read the Policies section on the course web site before
15-750 Graduate Algorithms Spring 2009
Miller and Dinitz and Tangwongsan Assignment 4 Solutions
1
Minimum Spanning Trees (25 pts.)
While we did not have time to cover them in class, minimum spanning t
This article was downloaded by: [Brown University] On: 2 November 2009 Access details: Access Details: [subscription number 784168975] Publisher Taylor & Francis Informa Ltd Registered in England and