São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Approximation Algorithms for Circle
Packing
Flvio K. Miyazawa
unicamp
So Paulo School of Advanced Science on
Algorithms, Combinatorics and Optimization
So Paulo, SP
July, 2016
Flvio K. Miyazawa
Approximation Algorithms for Circle Packing
July, 2016
1 / 57
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Approximation Algorithms for Circle
Packing
Flvio K. Miyazawa
unicamp
So Paulo School of Advanced Science on
Algorithms, Combinatorics and Optimization
So Paulo, SP
July, 2016
Flvio K. Miyazawa
Approximation Algorithms for Circle Packing
July, 2016
1 / 93
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Determining the rank of some graph
convexities
Jayme L Szwarcfiter
Federal University of Rio de Janeiro
State University of Rio de Janeiro
./
Purpose
Parameters related to graph convexities
Common graph convexities
Complexity results concerning the comput
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Recent Progress in Approximation Algorithms for
the Traveling Salesman Problem
Lecture 1: Some basic algorithms
David P. Williamson
Cornell University
July 1822, 2016
So Paulo School of Advanced Science on
Algorithms, Combinatorics, and Optimization
Davi
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Recent Progress in Approximation Algorithms for
the Traveling Salesman Problem
Lecture 4: st path TSP for graph TSP
David P. Williamson
Cornell University
July 1822, 2016
So Paulo School of Advanced Science on
Algorithms, Combinatorics, and Optimization
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
The regularity method and blowup lemmas for
sparse graphs
Y. Kohayakawa (So Paulo)
SPSAS Algorithms, Combinatorics and Optimization
University of So Paulo
July 2016
Partially supported CAPES/DAAD (430/15), CNPq (459335/20146, 310974/20135), and
FAPESP
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Harmonic analysis on polytopes and cones
So Paulo school of advanced science on algorithms,
combinatorics, and optimization
Friday, July 22, 2016
Sinai Robins
University of So Paulo
Lecture 4.
The discrete volume we would like to develop is the solid angl
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Recent Progress in Approximation Algorithms for
the Traveling Salesman Problem
Lecture 3: The st path TSP
David P. Williamson
Cornell University
July 1822, 2016
So Paulo School of Advanced Science on
Algorithms, Combinatorics, and Optimization
David P.
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Lecture 2.
Part I. History of tilings (1tilings)
Part II. Multitilings (ktilings), recent results
Part III. Harmonic analysis approaches/ideas
Part I. History of tilings (1tilings)
What kind of tilings?
Part I. History of tilings (1tilings)
What kind
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Recent Progress in Approximation Algorithms for
the Traveling Salesman Problem
Lecture 3: The st path TSP
David P. Williamson
Cornell University
July 1822, 2016
So Paulo School of Advanced Science on
Algorithms, Combinatorics, and Optimization
David P.
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Recent Progress in Approximation Algorithms for
the Traveling Salesman Problem
Lecture 2: Graph TSP
David P. Williamson
Cornell University
July 1822, 2016
So Paulo School of Advanced Science on
Algorithms, Combinatorics, and Optimization
David P. William
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
The regularity method and blowup lemmas for
sparse graphs
Y. Kohayakawa (So Paulo)
SPSAS Algorithms, Combinatorics and Optimization
University of So Paulo
July 2016
Partially supported CAPES/DAAD (430/15), CNPq (459335/20146, 310974/20135), and
FAPESP
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
The regularity method and blowup lemmas for
sparse graphs
Y. Kohayakawa (So Paulo)
SPSAS Algorithms, Combinatorics and Optimization
University of So Paulo
July 2016
Partially supported CAPES/DAAD (430/15), CNPq (459335/20146, 310974/20135), and
FAPESP
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Recent Progress in Approximation Algorithms for
the Traveling Salesman Problem
Lecture 2: Graph TSP
David P. Williamson
Cornell University
July 1822, 2016
So Paulo School of Advanced Science on
Algorithms, Combinatorics, and Optimization
David P. William
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
The regularity method and blowup lemmas for
sparse graphs
Y. Kohayakawa (So Paulo)
SPSAS Algorithms, Combinatorics and Optimization
University of So Paulo
July 2016
Partially supported CAPES/DAAD (430/15), CNPq (459335/20146, 310974/20135), and
FAPESP
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Recent Progress in Approximation Algorithms for
the Traveling Salesman Problem
Lecture 4: st path TSP for graph TSP
David P. Williamson
Cornell University
July 1822, 2016
So Paulo School of Advanced Science on
Algorithms, Combinatorics, and Optimization
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
So Paulo School of Advanced Science on Algorithms,
Combinatorics and Optimization
The Perfect Matching Polytope, Solid Bricks and
the Perfect Matching Lattice
July 2016
Cludio L. Lucchesi
FACOM , UFMS ,
Brazil
spsassco1 p. 1/33
Genesis
Theorem [Tait (18
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Graph limits and their applications
in extremal combinatorics
(Part 3)
Dan Kr
al
University of Warwick
S
ao Paulo
July 2016
1
Flag algebras
the flag algebra method independent of graph limits
we introduce the method using graphons for simplicity
algebra
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
So Paulo School of Advanced Science on Algorithms,
Combinatorics and Optimization
The Perfect Matching Polytope, Solid Bricks and
the Perfect Matching Lattice
July 2016
Cludio L. Lucchesi
FACOM , UFMS ,
Brazil
spsassco1 p. 1/50
4Flows
Theorem [Tait (18
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Graph limits and their applications
in extremal combinatorics
(Part 1)
Dan Kr
al
University of Warwick
S
ao Paulo
July 2016
1
Why limits?
asymptotic properties of large (discrete) objects
we implicitly use limits in our considerations anyway
How does th
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
So Paulo School of Advanced Science on Algorithms,
Combinatorics and Optimization
The Perfect Matching Polytope, Solid Bricks and
the Perfect Matching Lattice
July 2016
Cludio L. Lucchesi
FACOM , UFMS ,
Brazil
spsassco1 p. 1/21
The Precedence Relation
m
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
So Paulo School of Advanced Science on Algorithms,
Combinatorics and Optimization
The Perfect Matching Polytope, Solid Bricks and
the Perfect Matching Lattice
July 2016
Cludio L. Lucchesi
FACOM , UFMS ,
Brazil
spsassco4 p. 1/24
Open Problems
Is solidity
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Graph limits and their applications
in extremal combinatorics
(Part 4)
Dan Kr
al
University of Warwick
S
ao Paulo
July 2016
1
Flag algebras
algebra A of formal linear combinations of graphs
addition and multiplication by a scalar
homomorphism fW : A R f
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Graph limits and their applications
in extremal combinatorics
(Part 2)
Dan Kr
al
University of Warwick
S
ao Paulo
July 2016
1
Plan for today
Limits of dense graphs
recap of yesterdays lecture
existence of a limit graphon
graph quasirandomness
some other
São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization
INSTITUTE 100

Summer 2015
Graph limits and their applications
in extremal combinatorics
(Part 5)
Dan Kr
al
University of Warwick
S
ao Paulo
July 2016
1
Plan for today
Flag algebra method
quick recap
SDP formulation
Limits of hypergraphs
limit representation
Limits of permutatio