Problem Set #4 IE 495
Due October 6, 2000 1. Write pseudo-code for an implementation of a doubly linked list. The supported operations should include make_list() insert() delete() concatenate() split()
Specify the arguments for e
Problem Set #2 IE 495
Due September 18
Written Problems
1. Show that a recursive algorithm with running time satisfying T(1) = 1 T(n) = T(n - 1) + f(n) satisfies T(n) (n2) if f(n) (n). 2. The sequence of Fibonacci numbers, f1, f2, f3, . is defined
Computation in Operations Research IE 495
Dr. Ted Ralphs
First Meeting August 29, 2000
Administrivia
Class Meeting Time Introductions Surveys Office Hours
What is the motivation for this class?
"Here is your book, the one your thousands of
IE 495 Lecture 19 November 2, 2000
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 8 Grama and Kumar, Parallel Search Algorithms.
Parallel Branch and Bound
Divide and conquer approach "Obvious" approach to parallelization Paralleli
IE 495 Lecture 6
September 14, 2000
Reading for This Lecture
Primary
Paper by Kumar and Gupta Paper by Gustafson
Secondary
Roosta, Chapter 5
Analyzing Parallel Algorithms
Parallel Systems
A parallel system is a parallel algorithm plus a sp
IE 495 Lecture 26 December 5, 2000
Reading for This Lecture
Primary
See me if you want references
Example: Vertex Coloring
Upper Bound:
Order nodes by degree In order, color each node according to lowest feasible color
Lower Bound:
IE 495 Lecture 4
September 7, 2000
Reading for this lecture
Primary
Miller and Boxer, Chapters 2 and 3 Aho, Hopcroft, and Ullman, Sections 2.5-2.9
Induction and Recursion
Mathematical Induction
Induction is a technique for proving statements a
Computation in Operations Research IE 495
Dr. Ted Ralphs
First Meeting August 29, 2000
Administrivia
Class Meeting Time Introductions Surveys Office Hours
What is the motivation for this class?
"Here is your book, the one your thousands of
IE 495 Lecture 17 October 26, 2000
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 8
Search Algorithms
Integer Knapsack Problem
We are given n objects. Each object has a weight wi and a profit pi. We also have a knapsack with capac
IE 495 Lecture 6
September 14, 2000
Reading for This Lecture
Primary
Paper by Kumar and Gupta Paper by Gustafson
Secondary
Roosta, Chapter 5
Analyzing Parallel Algorithms
Parallel Systems
A parallel system is a parallel algorithm plus a sp
IE 495 Lecture 26 December 5, 2000
Reading for This Lecture
Primary
See me if you want references
Example: Vertex Coloring
Upper Bound:
Order nodes by degree In order, color each node according to lowest feasible color
Lower Bound:
IE 495 Lecture 19 November 2, 2000
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 8 Grama and Kumar, Parallel Search Algorithms.
Parallel Branch and Bound
Divide and conquer approach "Obvious" approach to parallelization Paralleli
Problem Set #3 IE 495
Due September 25
Written Problems
1. A binary relation on a set A is said to be an equivalence relation on A if it is reflexive, symmetric, and transitive, i.e. for all a, b, c A, a a, a b b a, and (a b) (b c) a c. Fu
IE 495 Lecture 15 October 19, 2000
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 4 Kozen, Lecture 3
Secondary
Miller and Boxer, Chapter 12 (up to page 286)
Baruvka's Algorithm
At each step, select all edges that connect some
Problem Set #4 IE 495
Due October 6, 2000 1. Write pseudo-code for an implementation of a doubly linked list. The supported operations should include make_list() insert() delete() concatenate() split()
Specify the arguments for e
Problem Set #1 IE 495
Due September 11
Written Problems
1. Explain how you could simulate a shared memory model of computation using a distributed memory model with one additional processor. [Hint: What does the interconnection network look like?] H
IE 495 Lecture 15 October 19, 2000
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 4 Kozen, Lecture 3
Secondary
Miller and Boxer, Chapter 12 (up to page 286)
Baruvka's Algorithm
At each step, select all edges that connect some
IE 495 Lecture 18 October 31, 2000 Happy Halloween!
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 8 Grama and Kumar, Parallel Search Algorithms.
Search Algorithms
Branch and Bound Methods
Branch and Bound is a general method tha
Problem Set #1 IE 495
Due September 11
Written Problems
1. Explain how you could simulate a shared memory model of computation using a distributed memory model with one additional processor. [Hint: What does the interconnection network look like?] H
Problem Set #2 IE 495
Due September 18
Written Problems
1. Show that a recursive algorithm with running time satisfying T(1) = 1 T(n) = T(n - 1) + f(n) satisfies T(n) (n2) if f(n) (n). 2. The sequence of Fibonacci numbers, f1, f2, f3, . is defined
IE 495 Lecture 18 October 31, 2000 Happy Halloween!
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 8 Grama and Kumar, Parallel Search Algorithms.
Search Algorithms
Branch and Bound Methods
Branch and Bound is a general method tha
IE 495 Lecture 11 October 3, 2000
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 2, Section 3 Kozen, Lectures 8-11
Binomial Trees
The binomial tree of rank i (Bi) is defined recursively. Bi consists of a root with i children B0 ,
IE 495 Lecture 4
September 7, 2000
Reading for this lecture
Primary
Miller and Boxer, Chapters 2 and 3 Aho, Hopcroft, and Ullman, Sections 2.5-2.9
Induction and Recursion
Mathematical Induction
Induction is a technique for proving statements a
IE 495 Lecture 14 October 17, 2000
Reading for This Lecture
Primary
Horowitz and Sahni, Chapter 4 Kozen, Lecture 3
Secondary
Miller and Boxer, Chapter 12 (up to page 286)
Spanning Trees
We are given a graph G = (V, E). A spanning tree of E
IE 495 Lecture 4
Stochastic Programming Recourse Models
Prof. Je Linderoth
January 22, 2003
January 22, 2003
Stochastic Programming Lecture 4
Slide 1
Outline
Formal notation for recourse models Second-stage value function Expected value function Forming
IE 495 Lecture 5
Stochastic Programming Math Review and MultiPeriod Models
Prof. Jeff Linderoth
January 27, 2003
January 27, 2003
Stochastic Programming Lecture 5
Slide 1
Outline
Homework questions? I would start on it fairly soon if I were you. A fairly
IE 495 Lecture 6
Stochastic Programming MultiPeriod Models
Prof. Jeff Linderoth
January 29, 2003
January 29, 2003
Stochastic Programming Lecture 6
Slide 1
Outline
Homework questions? (I haven't started it yet either). I won't be in my office after class
IE 495 Lecture 7
Stochastic Programming Multistage Models and (S)MPS
Prof. Jeff Linderoth
February 3, 2003
February 3, 2003
Stochastic Programming Lecture 7
Slide 1
Outline
Multi-stage problems. The "tree" version Creating Stochastic Programming Instance
IE 495 Lecture 9
Properties of the Recourse Function
Prof. Jeff Linderoth
February 10, 2003
February 5, 2003
Stochastic Programming Lecture 9
Slide 1
Outlinea
Two-stage stochastic LP Convexity Continuity Differentiability Optimality Conditions L-Shaped M
IE 495 Lecture 10
Properties of the Recourse Function
Prof. Jeff Linderoth
February 12, 2003
February 10, 2003
Stochastic Programming Lecture 10
Slide 1
Today's Topic
M E T H O D
February 10, 2003
Stochastic Programming Lecture 10
Slide 2
Outline
Small a