CSE 541 Advanced Algorithms
September 22, 2016
Homework 2 Practice Problems
Below is a set of practice problems on designing and proving the correctness of greedy algorithms, to
help you check your understanding of the approach weve discussed in class.
Yo
CSE 541 Advanced Algorithms
September 6, 2016
Homework 1 Practice Problems
Below is a set of practice problems on designing and proving the correctness of greedy algorithms, to
help you check your understanding of the approach weve discussed in class.
You
CSE 541 Advanced Algorithms
September 22, 2016
Homework 2 Practice Problem Solutions
WARNING: if you havent at least tried hard to solve the practice problems before reading these solutions,
you are missing the point. If you cant make any progress, talk t
CSE 541 Advanced Algorithms
September 6, 2016
Homework 1 Practice Problem Solutions
WARNING: if you havent at least tried hard to solve the practice problems before reading these solutions,
you are missing the point. If you cant make any progress, talk to
CSE 541 Advanced Algorithms
Fall Semester 2016
Homework 2: Dynamic Programming
Assigned: 9/22/2016
Due Date: 10/6/2016
This homework must be completed and submitted electronically. Formatting standards, submission
procedures, and (optional) document templ
CSE 541 Advanced Algorithms
Fall Semester 2016
Homework 1: Greedy Algorithms
Assigned: 9/6/2016
Due Date: 9/20/2016
This homework must be completed and submitted electronically. Formatting standards, submission
procedures, and (optional) document template
CSE 541 Advanced Algorithms
September 26, 2016
Homework 2 Solutions
Nota bene: there are often multiple correct decompositions to solve a problem by dynamic programming. I
have picked one for each problem, but just because it doesnt look like yours doesnt
CSE 541 Advanced Algorithms
October 18, 2016
Homework 3 Solutions
Nota bene: the reductions given here are all from the suggested problems. There are undoubtedly other
correct reductions from different problems you could use instead.
1. We first show that
CSE 541 Advanced Algorithms
September 21, 2016
Homework 1 Solutions
1. The given algorithm is indeed optimal.
First, observe that, without loss of generality, we need consider only schedules that use all slots
[0, 1, . . . n 1]. Any schedule without this
CSE 541 Advanced Algorithms
Fall Semester 2016
Homework 3: NP Completeness
Assigned: 10/13/2016
Due Date: 10/27/2016
This homework must be completed and submitted electronically. Formatting standards, submission
procedures, and (optional) document templat
CSE541 Class 6
Jeremy Buhler
September 15, 2016
Today: dynamic programming, round 2 (also, linear algebra)
1
A Mathematical Conundrum
Who here has used MATLAB?
Its a program for doing math with matrices!
(Recall that an m n matrix A is a 2D array of nu
CSE 541 Advanced Algorithms
August 29, 2016
Course Overview and General Information
Your primary source for class information, homeworks, and handouts is the class web site, http:/classes.
engineering.wustl.edu/cse541. Please check this site regularly for
CSE 441T/541T Advanced Algorithms
September 9, 2011
Framework for Design of Greedy Algorithms
Greedy algorithms for combinatorial optimization typically share a common structure. It helps
to keep this structure in mind when you are trying to design and pr
CSE 441T/541T Advanced Algorithms
October 12, 2011
Proving Decision Problems NP-Complete
NP-completeness is a useful concept for showing the diculty of a computational problem, by
showing that the existence of a polynomial-time algorithm for the problem w
CSE 441T/541T Advanced Algorithms
September 22, 2010
Framework for Design of Dynamic Programming Algorithms
Dynamic programming algorithms for combinatorial optimization generalize the strategy we studied
for design and analysis of greedy algorithms. To b
CSE 441T/541T Advanced Algorithms
October 26, 2012
Exam 2 Practice Problem Solutions
WARNING: if you havent at least tried hard to solve the practice problems before reading these
solutions, you are missing the point. If you cant make any progress, talk t
CSE 441/541 - NP Completeness
Weixiong Zhang
October 1 2012
This is something completely dierent from what we have seen so far!
1
First Things First - Basic Concepts
1.1
Decision Problems
Were going to look at some important, not-quite optimization proble
CSE 441/541 - Linear Programming
Weixiong Zhang
November 26, 2012
1
A Dierent Kind of Problem
Lets go back for a bit to problems that can be solved optimally in polynomial
time.
You are developing a new fad diet.
To plan a menu, you have a list of n foo
CSE 441/541 - Dynamic Programming
Weixing Zhang
1
First, a Simple, But Not So Easy Problem of
Shortest Path
2
A Mathematical Conundrum
Who here has used MatLab?
Its a program for doing math with matrices!
(Recall that an nm matrix A is a 2D array of nu
CSE 441/541 - Approximation
Weixiong Zhang
October 24, 2012
NP-hardness does not mean you can give up!
1
Motivation Approximation
What do you do if you want to solve an NP optimization problem?
Idea 1: use an exponential-time algorithm.
If your inputs
CSE 541 Advanced Algorithms
November 1, 2016
Homework 4 Practice Problems
Below is a set of practice problems on NP-completeness and approximation to help you check your understanding of the approaches weve discussed in class.
You can find solutions to th
CSE 541 Advanced Algorithms
Fall Semester 2016
Homework 4: More NP-Completeness, and Approximation Algorithms
Assigned: 11/1/2016
Due Date: 11/15/2016
This homework must be completed and submitted electronically. Formatting standards, submission
procedure
CSE541 Class 2
Jeremy Buhler
September 1, 2016
1
A Classic Problem and a Greedy Approach
A classic problem for which one might want to apply a greedy algo is knapsack.
Given: a knapsack of capacity M , and n items.
Item i has weight wi > 0, value vi > 0
CSE541 Class 14
Jeremy Buhler
October 20, 2016
1
A Widget, It Has Got a Widget.
Reductions to show the hardness of graph-related problems sometimes involve building
very problem-specific graph families. These are often called widgets.
Example: 3-coloring
CSE541 Class 19
Jeremy Buhler
November 8, 2016
1
A Different Kind of Problem
Lets go back for a bit to problems that can be solved optimally in polynomial time.
You are developing a new fad diet.
To plan a menu, you have a list of n foods to choose from
CSE541 Class 5
Jeremy Buhler
September 13, 2016
1
Problem: Longest Common Subsequence
Lets do some stringology!
Consider the problem of diffing two text files X and Y , each consisting of zero or
more lines.
To diff X and Y , we first find an ordered li
CSE541 Class 10
Jeremy Buhler
September 29, 2016
1
Definition of Reduction
Even if I cant prove a problem hard in an absolute sense, I can prove that it is at least
as hard as another problem.
Let L and L0 be two decision problems.
Say that L0 polynomia
CSE541 Class 20
Jeremy Buhler
November 11, 2016
1
2-Machine Scheduling With Costs
Lets consider new variant of multiprocessor scheduling problem.
Given set of n jobs.
Each job must be run on one of two machines (m = 2).
Jobs cannot be split across mach