Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
,5
CMPUT 675: Approximation Algorithms
Fall 2013
Lecture 4, 5 (Sep 17, Sep 19, 2013 ): Set Cover, LP Duality, 01 Knapsack
Lecturer: Mohammad R. Salavatipour
Scribe: Afshin Are, Based on older notes
This week we see two other algorithms for approximating
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 18&19: Iterative relaxation
Lecturer: Mohammad R. Salavatipour
Date: Nov 5, 2009
Scriber: Zhong Li
1 Spanning Tree Polytope
Last lecture we started studying the following L
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 12,13: Flows and Circulations, Matroids
Lecturer: Mohammad R. Salavatipour
Date: Oct.1315, 2009
1
Scriber: Michael Joya
Flows and Circulations contd
This lecture builds on
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 1617: Matroid Intersection
Lecturer: Mohammad R. Salavatipour
Date: Oct 25,27, 2009
Scriber: Yining Wang
1 Matroid Intersection
We have seen that greedy algorithm works we
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 1: Basics, Bipartite Matching
Lecturer: Mohammad R. Salavatipour
Date: Sept 3, 2009
Scriber: Mohammad R. Salavatipour
This lecture starts with some basic notions. Then we s
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 10,11: General Matching Polytope, Maximum Flow
Lecturer: Mohammad R. Salavatipour
Date: Oct 6 and 8, 2009
Scriber: Mohammad Reza Khani
In this lecture we nish the discussio
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 2: Cardinality Matching, Maximum Weighted matching
Lecturer: Mohammad R. Salavatipour
Date: Sept 8 and 10, 2009
Scriber: Siamak Ravanbakhsh
This lecture continues the discu
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 6,7: Linear Programming, Simplex method
Lecturer: Mohammad R. Salavatipour
Date: Sept 22 and 24, 2009
Scriber: Yining Wang
This lecture starts with some basic notions. Then
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecture 4: Primal Dual Matching Algorithm and NonBipartite Matching
Lecturer: Mohammad R. Salavatipour
Date: Sept 15 and 17, 2009
Scriber: Idanis Diaz
We start by recalling the fo
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
University of Alberta
Department of Chemical and Materials Engineering
CHE 694
Advanced Optimization for Process Systems Engineering
Fall 2016
Instructor: Zukui Li
Time and Location: M, W, F, 9:009:50am, ETLC 1018
Contact: 7804921107, Email: zukui@ual
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009)
Lecturer: Mohammad R. Salavatipour
Date: Oct 2022, 2009
Scriber: Siamak Ravanbakhsh
This lecture continues our previous discussion on matroids. This includes some new denitions an
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
CMPUT 675: Approximation Algorithms
Fall 2011
Lecture 16 (Nov 1, 2011 ): Approximation of metrics by Tree metrics
Lecturer: Mohammad R. Salavatipour
16.1
Scribe: Amritpal Saini
Introduction
A common and useful technique to simplify some problems given in
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
13
CMPUT 675: Approximation Algorithms
Fall 2011
Lecture 1213, (Oct. 18 and 20, 2011): MST, Mincost Bounded Degree ST
Lecturer: Mohammad R. Salavatipour
12.1
Scribe: Xida Chen
Minimum Spanning Tree
Recall the following LP relaxation for the Minimum Spa
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
CMPUT 675: Approximation Algorithms
Fall 2013
Lecture 1 (Sept 5, 2013): Introduction, Vertex Cover
Lecturer: Mohammad R. Salavatipour
1.1
Scribe: Mohammad R. Salavatipour
Introduction
In this course we will be studying how to design approximation algorith
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
,3
CMPUT 675: Approximation Algorithms
Fall 2013
Lecture 2,3 (Sept 10 and 12, 2013): TSP, Set Cover, Introduction to LP
Lecturer: Mohammad R. Salavatipour
2.1
Scribe: Tim Yee, Bing Xu and older notes
Traveling Salesman Problem (TSP)
This is a very wellkn
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
and 11 (Oct 8,10)
CMPUT 675: Topics on Approximation Algorithms and Approximability
Fall 2013
Lecture 10 and 11 (Oct 8,10): Multiway Cut, Multicut
Lecturer: Mohammad R. Salavatipour
10.1
Scribe: Yaochen Hu and older notes
Multiway Cut
Denition 10.1 In a G
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
CMPUT 675: Approximation Algorithms
Fall 2011
Lecture 18 (November 8): Euclidean TSP
Lecturer: Mohammad R. Salavatipour
18.1
Scribe: Seyed Sina Khankhajeh
Introduction
Euclidean TSP is a subset of Travelling Salesman Problem in which distances are on Eucl
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
,7
CMPUT 675: Topics on Approximation Algorithms and Approximability
Fall 2013
Lecture 6,7 (Sep 24 and 26,2013):Bin Packing, Facility Location, KCenter
Lecturer: Mohammad R. Salavatipour
6.1
Scribe: Rohit Sivakumar and old scribes
Bin Packing
The problem
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
CMPUT 675: Approximation Algorithms
Fall 2013
Lecture 12 (Oct 15, 2013 ): Approximation via rounding SDP: MaxCut
Lecturer: Mohammad R. Salavatipour
12.1
Scribe: based on older notes
Approximation Algorithm for MaxCut
The next technique we learn is desig
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
,20
CMPUT 675: Approximation Algorithms
Fall 2011
Lecture 19,20 (Nov 15&17, 2011): Hardness of Approximation, PCP theorem
Lecturer: Mohammad R. Salavatipour
19.1
Scribe: based on older notes
Hardness of Approximation
So far we have been mostly talking abo
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Summer 2014
,9
CMPUT 675: Approximation Algorithms
Fall 2013
Lecture 8, 9 (Oct 1 and 3): kmedian, and Steiner forest
Lecturer: Mohammad R. Salavatipour
8.1
Scribe: based on older notes
kmedian problem
kmedian is an important clustering problem that has similaritie
Topics in Algorithms and Combinatorial Optimization
CMPUT 675

Fall 2012
Convex Set
1
Definition of convex set
Definition 1 (Line) Let the vectors x1 , x2 Rn . The line through x1 and x2 is defined as the set
cfw_xx = (1 )x1 + x2 , R
(1)
Definition 2 (Line segment) Let the vectors x1 , x2 Rn . The closed line segment through