A semidefinite programming hierarchy for geometric packing problems David de Laat (TU Delft) Joint work with Frank Vallentin (Universit¨at zu K¨oln) Isaac Newton Institute for Mathematical Sciences – July 2013

Source URL: www.daviddelaat.nl

• Graph theory
• NP-complete problems
• Discrete geometry
• Independent set
• FranklRdl graph
• Lovsz number

Moment methods in energy minimization David de Laat Delft University of Technology (Joint with Fernando Oliveira and Frank Vallentin) L´aszl´

Source URL: www.daviddelaat.nl

• Operations research
• Discrete geometry
• NP-complete problems
• Conjectures
• Circle packing
• Sphere packing
• Independent set
• Kepler conjecture
• Tammes problem
• Mathematical optimization
• Semidefinite programming
• FranklRdl graph

Online Optimization of Busy Time on Parallel Machines∗ Mordechai Shalom1 Ariella Voloshin2 Prudence W.H. Wong3 Fencol C.C. Yung3 Shmuel Zaks2

Source URL: cgi.csc.liv.ac.uk

• Scheduling
• Operations research
• Mathematical optimization
• Combinatorial optimization
• Independent set
• Interval scheduling
• Interval graph
• Bin packing problem
• Algorithm
• Steve Jobs
• Job shop scheduling
• Multiprocessor scheduling

393 Documenta Math. On Packing Spheres into Containers About Kepler’s Finite Sphere Packing Problem

Source URL: documenta.sagemath.org

• Convex analysis
• Convex set
• Convex hull
• Limit of a function

Moment methods in energy minimization David de Laat CWI Amsterdam Andrejewski-Tage Moment problems in theoretical physics

Source URL: www.daviddelaat.nl

• Operations research
• Discrete geometry
• NP-complete problems
• Conjectures
• Circle packing
• Sphere packing
• Independent set
• Kepler conjecture
• Tammes problem
• Mathematical optimization
• Semidefinite programming
• FranklRdl graph

A semidefinite programming hierarchy for packing problems in discrete geometry David de Laat (TU Delft) Joint work with Frank Vallentin (Universit¨at zu K¨oln) Applications of Real Algebraic Geometry

Source URL: www.daviddelaat.nl

• NP-complete problems
• Operations research
• Independent set
• Optimization problem
• Discrete geometry
• Graph
• Duality
• Packing problems
• Mathematical optimization
• Planar graphs
• Matching
• Matroid

An ant colony optimization inspired algorithm for the Set Packing Problem with application to railway infrastructure Xavier GANDIBLEUX1 , Julien JORGE1 , S´ ebastien ANGIBAUD1 Xavier DELORME2 and Joaquin RODRIGUEZ3

Source URL: www.emse.fr

• Institut national de recherche sur les transports et leur scurit
• Universit Lille Nord de France
• Ant colony optimization algorithms

CCCG 2007, Ottawa, Ontario, August 20–22, 2007 Disjoint Segments have Convex Partitions with 2-Edge Connected Dual Graphs Nadia M. Benbernou∗

Source URL: www.eecs.tufts.edu

• Planar graphs
• Graph connectivity
• Graph operations
• Dual graph
• Line segment
• Cut
• Convex set
• Connectivity
• Graph
• Bridge
• Planar separator theorem
• Circle packing theorem

OPTIMAL COVERS WITH HAMILTON CYCLES IN RANDOM GRAPHS ¨ DAN HEFETZ, DANIELA KUHN, JOHN LAPINSKAS AND DERYK OSTHUS Abstract. A packing of a graph G with Hamilton cycles is a set of edgedisjoint Hamilton cycles in G. Such

Source URL: web.mat.bham.ac.uk

Chapter 10 Bin Packing Here we consider the classical Bin Packing problem: We are given a set I = {1, . . . , n} of items, where item i ∈ I has size si ∈ (0, 1] and a set B = {1, . . . , n} of bins with capacity one

Source URL: www2.informatik.hu-berlin.de

• Computational complexity theory
• Theory of computation
• Complexity classes
• Packing problems
• NP-complete problems
• Bin packing problem
• Approximation algorithms
• Polynomial-time approximation scheme
• Partition problem
• NP
• NC
• Time complexity