Thomas M. Liebling

École Polytechnique Fédérale de Lausanne | EPFL · Mathematics Section

This issue contains papers presented at the Sixth Latin-American Algorithms, Graphs, and Optimization Symposium LAGOS’11 held March 28th–April 1st, 2011, in Bariloche, Argentina. During LAGOS’11, the 30th anniversary of the publication of the seminal paper by M. Grötschel, L. Lovász, and A. Schrijver, “The Ellipsoid Method and its Consequences in C...

We consider the problem of optimizing a novel acoustic leakage detection system for urban water distribution networks. The system is composed of a number of detectors and transponders to be placed in a choice of hydrants such as to provide a desired coverage under given budget restrictions. The problem is modeled as a particular Prize-Collecting St...

In this paper we show that separation from membership for well defined non empty polyhedra can be considered to lie in the folklore of mathematical programming.

What is the influence of sand grain shapes on an hourglass accuracy, and how does it affect the jamming probability? We study such a question using numerical simulation and our recently introduced spheropolyhedral particles. Spheropolyhedra constitute a very rich class of shapes that naturally generalize the traditional spheres used in the Distinct...

We study the flow of grains in a bi‐dimensional hopper. We propose a simple continuous probabilistic flow model: from uniformly random positions in the hopper, particles evolve without interaction towards the hopper aperture and jamming occurs if sufficiently many simultaneously try to exit. Using the more elaborate DEM simulations as a benchmark...

The Distinct Element Method (DEM) is a popular tool to perform granular media simulations. The two key elements this requires are an adequate model for inter-particulate contact forces and an efficient contact detection method. Originally, this method was designed to handle spherical-shaped grains that allow for efficient contact detection and simp...

We describe an approach for exploring microscopic properties of granular media that couples x-ray microtomography and distinct-element-method (DEM) simulations through image analysis. We illustrate it via the study of the intriguing phenomenon of instant arching in an hourglass (in our case a cylinder filled with a polydisperse mixture of glass bea...

Granular media composed of elongated particles rearrange and order vertically upon vertical vibration. We perform pseudo-two-dimensional discrete element model simulations and show that this phenomenon also takes place with no help from vertical walls. We quantitatively analyze the sizes of voids forming during vibrations and consider a void-fillin...

We describe particular paths in the flip-graph of regular triangulations in any dimension. It is shown that any pair of regular triangulations is connected by a path along which none of their common faces are destroyed. As a consequence, we obtain the connectivity of the flip-graph of regular triangulations that share the same vertex set.

We study the jamming of bead assemblies placed in a cylindrical container whose bottom is pierced with a circular hole. Their jamming behavior is quantified here by the median jamming diameter, that is the diameter of the hole for which the jamming probability is 0.5. Median jamming diameters of monodisperse assemblies are obtained numerically usin...

We consider the school bus routing and scheduling problem, where transportation demand is known and bus scheduling can be planned in advance. We present a comprehensive methodology designed to support the decision of practitioners. We first propose a modeling framework where the focus is on optimizing the level of service for a given number of buse...

We address the weighted max-cut problem, or equivalently the problem of maximizing a quadratic form in n binary variables. If the underlying (symmetric) matrix is positive semidefinite of fixed rank d, then the problem can be reduced to searching the extreme points of a zonotope, thus becoming of polynomial complexity in O(nd − 1). Reverse search i...

We present a three-dimensional distinct element model (DEM) able to handle populations of spherocylinders. We report on granular crystallization occurring when vibrating mono-disperse assemblies of spherocylinders that faithfully reproduce the corresponding results of physical experiments from the literature.

The distinct element method was originally designed to handle spherical particles. Here, this method is generalized to a wider range of particle shapes called spherosimplices. A contact detection method is given as well which uses weighted Delaunay triangulations to detect contacts occurring in a population of particles with such shapes. Finally, a...

Homogenous granular media composed of spherocylindrical rods rearrange and order vertically upon vibration. Performing pseudo-bidimensional experiments and simulations, we isolated void-filling mechanism as a cause for this phenomenon, independently of wall influence. Our discrete element model (DEM) faithfully captures the physical behavior. Simul...

We survey results about the facial structure of the stable set polytope for variants of claw-free graphs.

We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles and Trotter [7] by (i) showing that for any nonnegative integer a there exists a circulant graph whose stable set polytope has a facet-inducing inequality with (a,a+1)-valued coefficients (rank facets have only coefficients 0, 1), and (ii) provid...

Proceedings of Latin-Amercian Conference on Combinatorics, Graphs and Applications, University of Chile - Santiago, Chile - August 16-20, 2004

Meshes with (recursive) subdivision connectivity, such as subdivision surfaces, are increasingly popular in computer graphics. They present several advantages over their Delaunay-type based counterparts, e.g., Triangulated Irregular Networks (TINs), such as efficient processing, compact storage and numerical robustness. A mesh having subdivision co...

Permettant la conception et l'entretien de systèmes logistiques et techniques toujours plus complexes, la recherche opérationnelle fait aujourd’hui partie du bagage essentiel à tout ingénieur. Avec un formalisme mathématique réduit, ce livre offre une introduction aux principaux outils de modélisation et de résolution des problèmes de recherche opé...

We consider the school bus routing and scheduling problem, where transportation demand is known and bus scheduling can be planned in advance, We first propose a modeling framework which aims to optimize a level of service for a given number of buses. Then, we describe a procedure building first a feasible solution, and subsequently improving it, us...

The distinct element method (DEM) is an approach to modelling and simulation well suited to the study of discontinuous phenomena. By tracking each element individually and dealing explicitly with every interaction among the elements, the DEM allows one to deduce statistical behaviour of the assembly. Realistic simulation of granular materials has l...

This paper presents a linear running time optimization algorithm for meshes with subdivision connectivity, e.g., subdivision surfaces. The algorithm optimizes a model using a metric defined by the user. Two functionals are used to build the metric: a rate functional and a distortion (i.e. error) functional. The distortion functional defines the err...

We first describe the three-dimensional extension of the molecular-dynamics models for granular media simulations. We then discuss the known energy dissipation problem occurring when simulating dense granular media with the usual molecular-dynamics forces models. We finally propose a force model able to control the energy dissipation in the multipa...

Computer simulations of granular materials based on the distinct element method (DEM) are now commonly used in the design and optimization of industrial processes. One of the leading mathematical approach to DEM uses dynamic triangulations for detecting collisions among moving spheres, and relies on advanced data structures and on the exact numeric...

We consider the school bus routing and scheduling problem, where transportation demand is known and bus scheduling can be planned in advance. We present a comprehensive methodology designed to support the decision of practitioners. We first propose a modeling framework where the focus is on optimizing the level of service for a given number of buse...

This article is to be publised as a chapter in the Padberg Festschrift "The Sharpest Cut" in the MPS-SIAM series on Optimization. 1 Introduction The unconstrained quadratic maximization problem in zero-one variables (abbreviated by 01QP) max f(x) = x T Qx subject to x # {0, 1} n , where Q is an n

Unconstrained zero-one quadratic maximization problems can be solved in polynomial time when the symmetric matrix describing the objective function is positive semidefinite of fixed rank with known spectral decomposition.

We present computational results when computing approximations of a class of meshes with subdivision connectivity, known as 4-8 meshes. We consider algorithms using vertex decimation or vertex insertion. We explain that a full decomposition of a 4-8 mesh using global error can be obtained with an ##n ### n# decimation algorithm. Our algorithm produ...

Meshes with subdivision connectivity are popular in applications such as visualization and finite element analysis. We consider a particular class of such meshes known as 4-8 meshes. We present computational results when computing approximations of 4-8 meshes using vertex decimation or vertex insertion. We first use our results to show that algorit...

Computer simulations of granular materials are often based on the Distinct Element Method (DEM) where each grain is considered individually. Since large quantities of grains are required to perform realistic experiments, high performance computing is mandatory. This paper presents the basis of the DEM, a sequential algorithm for spherical grains in...

This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise flat, triangulated surface. Based on properties of such structures, a generalized flip algorithm to construct the Delaunay triangulation and Voronoi diagram is presented. An application to biological membrane growth modeling is...

Computer simulations of granular materials are often based on the Distinct Element Method (DEM) where each grain is considered individually. Since large quantities of grains are required to perform realistic experiments, high performance computing is mandatory. This paper presents the basis of the DEM, a sequential algorithm for spherical grains in...

Given quadratic functionfthe unconstrained quadratic zero-one programming problem consists in minimizingf (x)wherexis a zero-one vector of dimension n. This problem is NP-hard and therefore the most efficient results have been obtained by heuristics. As optimal solutions are in most cases unkown, comparisons between heuristics are usually based on...

In this paper we address the problem of computing a minimal representation of the convex hull of the union of kH-polytopes in . Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is done by projecting the polytopes onto the two-dimensional space and solving a linear program. T...

This paper presents a robust and efficient parameter identification method of generalized profiles for motif recognition in biomolecular sequences. It is based on solving a non linear optimization problem that uses samples of positive as well as of negative sequences. Particular care is taken to enhance discriminating power by including over-fittin...

We present an efficient method for the computer simulation of granular media based on dynamic triangulations. Round and polygonal grains are considered. In both cases, we explain the theoretical principles on which the methods are based. The simulation schemes are outlined and several examples are given.

In this paper we present a heuristic algorithm for the well-known Unconstrained Quadratic 0–1 Programming Problem. The approach is based on combining solutions in a genetic paradigm and incorporates intensification algorithms used to improve solutions and speed up the method. Extensive computational experiments on instances with up to 500 variables...

This paper deals with a new discrete event simulation modeling concept, calledqobj, which comes from two well-known paradigms:objects andqueuing networks. The first provides important conceptual tools for model organization, while the second one allows for nice visualization of models' internal state and processes. Thanks to the integration of thes...

This paper deals with a new discrete event simulation modeling concept, calledqobj, which comes from two well- known paradigms:objects andqueuing networks. The first provides important conceptual tools for model organization, while the second one allows for nice visualization of models' internal state and processes. Thanks to the integration of the...

The diameter of a graph is the maximum length of shortest paths between two vertices in the graph. It has some interesting theoretical properties, as well as a practical use as the lower or upper bound for various graph-based algorithms. Many methods to compute the diameter exist, and they can be classified in two categories: manipulation of the di...

Given a set P of n points in the plane, we want to find a simple, not necessarily convex, pentagon Q with vertices in P of minimum area. We present an algorithm for solving this problem in time O(nT(n)) and space O(n) , where T(n) is the number of empty triangles in the set.

In this paper, we investigate the applicability of backtrack technique to solve the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack algorithm for the face enumeration problem whose space complexity is polynomial in the input s...

We propose a novel and poweful methodology for three- dimensional (3D) grain growth modelling in both the anisotropic and the locally inhomogeneous cases, thus significantly generalizing previous related two-dimensional work. The fundamental modelling structures for the polycrystals and their behaviour are dynamically evolving Laguerre diagrams in...

We review the general notion of Voronoi partitions of a given space and corresponding dual Delaunay tessellations. The classical flip algorithm is generalized to Laguerre partitions and to Voronoi partitions of piecewise linear surfaces and tori. Further, the utility of this notion is illustrated in the context of various simulation models of dynam...

This paper treats a production planning problem in an aluminum manufacturing plant characterized by milling equipment subject to wear and replacement, furnaces with limited capacities and precedence rules and timing implied by temperatures and alloy types. We describe a rule-driven mathematical model and present an efficient rolling horizon schedul...

Colliding beams experiments in High Energy Physics rely on solid state detectors to track the flight paths of charged elementary particles near their primary point of interaction. Reconstructing tracks in this region requires, per collision, a partitioning of up to 103 highly correlated observations into an unknown number of tracks. We report on th...

The basic concepts of a deterministic scheme for simulating grain growth or foam coarsening in two dimensions have been presented in Part I. Implementation of the corresponding Laguerre (or weighted Voronoi) diagram in computer manageable practical terms is now presented. The internal constituents of the model are discussed first and include the in...

The basic concepts of a deterministic model for simulating grain growth or foam coarsening in two dimensions are presented, and the fundamental tools necessary for its implementation into computer codes are provided. It is assumed that the actual cell structure can be satisfactorily represented by a Laguerre (or weighted Voronoi) diagram, entirely...

An efficient implementation of Cundall's model on the Cray T3D massively parallel computer is presented. This model is used to simulate granular media where every grain is identified separately, generating very time-consuming simulations. First, we show a data structure based on a triangulation which defines a neighbourhood of each grain. This allo...

We present a simple constructive heuristic for the optimal enclosed area polygon problem. Namely, given a finite set S of points in the plane, we look for the simple polygon with vertex set S having minimal, respectively maximal, enclosed area.

Polycrytalline structures are modeled via dynamically envolving power i.e. Laguerre diagrams in the three dimensional flat torus. Generating sites follow motion equations resulting from total (interface) enregy minimization., this results in an evolution of the associated structures with accompanying elementary topological tranformations. First com...

The 3D Laguerre model for polycrystal normal grain growth is generalized to the anisotropic case. In the model, the specific grain boundary energy id determined by the misorientation of adjacent grains and the grain boundary mobility is assumed to be isotropic. Preliminary simulation results show that the anisotropic model can reproduce the normal...

The distinct element method used to simulate behavior of granular media intrinsically needs a lot of computation. We developed a data structure based on a weighted Delaunay triangulation to efficiently detect collisions between a large number of discs. This triangulation is locally maintained in the course of time. It defines an implicit neighborho...

We present anO(p n) algorithm for the problem of finding disjoint simple paths of minimum total length betweenp given pairs of terminals on oriented partial 2-trees withn nodes and positive or negative arc lengths. The algorithm is inO(n) if all terminals are distinct nodes. We characterize the convex hull of the feasible solution set for the casep...

Given n pairs of points in the Euclidean plane, we address the problem of finding paths of minimum length linking the pairs that can be made disjoint by infinitesimal deformations. We present and compare several fast heuristics and their implementation. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 19...

The organization of refurbishment is a complex problem involving both physical and social constraints. Our purpose is to develop a computer aided tool to schedule renovation tasks. This paper presents an original methodology to generate and schedule renovation tasks according to constructional constraints and following a given strategy correspondin...

To investigate morphogenesis and in particular circularization mechanisms in young mycelia, we observe cultures of the zygomycete Mucor spinosus and develop discrete models of two-dimensional filamental branching growth. The models are based on the hypothesis that the fungus secretes a regulatory substance that diffuses into the surrounding medium...

We give a complete polyhedral characterization of the tree polytope (convex hull of the characteristic vectors of trees in the graph) on 2-trees.

This paper presents a sketch of a method useful in numerical simulations to efficiently manage motions and collisions of polygonal grains in the plane. This method uses a triangulation of the space between the polygons and it efficiently maintains its coherence in the course of time. This triangulation allows the calculation of exact times of colli...

Laguerre diagrams are used as a geometric idealization of 3-dimensional polycrystals. These cell structures are entirely defined by a set of weighted sites. Each site is given an additional weight which affects the size of the associated cell. Models of growth can be constructed for this idealized polycrystal geometry by writing the motion equation...

We model the problem of assigning referees to matches of volleyball championships as a combinatorial optimization problem. To solve it, we adapt three local search heuristics and study their behavior as a funtion of their parameters. We show the limitations of these algorithms and that the use of refined initialization algorithms and an "endgame" s...

The equipartition problem on an undirected graph G=(V,E), with n nodes and a system of edge weights, is to find a subset of [n/2] nodes such as the associate cut has the smallest cost. We present a polynomial algorithm to solve the equipartition problem on a series-parallel graph.

A set of Al2O3 samples were superplastically crept or stress-free annealed in identical conditions. Detailed quantitative microstructural evaluations of: grain sizes, shapes, orientations, coordination number and their distributions, were performed as well as determination od pair correlations of grain center coordinates. Small but presumably real...

Laguerre (or weighted Voronoi) diagrams are used as geometric idealization of 2-d polycrytals. The approximation is satisfactory. These cell structures are entirely defined by a set of weighted sites, and their motion (including the induced topological transformations) is transferred to that of the sites. Grain growth is modelled by solving a speci...

Stochastic models for the analysis of the energy and thermal comfort performances of passive solar devices have benn increasingly studied for over a decade. A new approach to thermal building modelling, based on Markov chains, is proposed here to combine both the accuracy of traditional dynamic simulation with the practical advantages of simplified...

We characterize the optimal reordering policies for the stationary periodic review AHM inventory model when there is a quick and a — generally cheaper — slow supplier, whose delivery lags differ by one period and whose fixed and unit ordering costs are arbitrary, as generalized (s,S) policies described by four parameters (s 1,S 1,s 2,S 2). Computat...

The placement of telecommunication satellites in the geostationary orbit (GSO) gives rise to NP-hard optimization problems usually approached with iterative neighborhood (possibly tabu) search schemes. A typical iteration thereof consists in fixing an order for the satellites and determining their actual locations by linear programming. In such pro...

Dans cet article, on présente le problème du calcul et de l'utilisation de plans de travail pour des monteurs responsables de la maintenance d'installations réparties dans une région donnée. Ce problème a été traité dans le cadre concret de la planification de la maintenance d'ascenseurs pour une grande entreprise Suisse. Cependant, la méthodologie...

The equipartition problem on an undirected graph G=(V,E) with n nodes and a system of edge weights, is to find a subset of [n/2] nodes such as the associate cut has a smallest cost. We present a polynomial algorithm to solve the equipartition problem on a tree.

This is a project carried out jointly by the EPFL and a large manufacturing group to set up a computer- aided system of production planning and control at the operational level in an aluminium foundry.