An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects

The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a stable matching of students to projects (and lecturers). However, these stable matchings can have different sizes, and the problem of finding a maximum stable matching (MAX-SPA-P) is NP-hard. There are two known approximation algorithms for MAX-SPA-P, with performance guarantees of 2 and 32 . In this paper, we describe an Integer Programming (IP) model to enable MAX-SPA-P to be solved optimally. Following this, we present results arising from an empirical analysis that investigates how the solution produced by the approximation algorithms compares to the optimal solution obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. Our main finding is that the 32 -approximation algorithm finds stable matchings that are very close to having maximum cardinality

Shared Heritage Revisited: National and Postnational Dimensions on the Example of Germans, Palestinians and Israelis

Culture is constructed, negotiated, managed, and shared by various ideological, political, and moral reasonings which manifest themselves tangibly and intangibly in public monuments, architecture, memorial sites, theaters, museums, orchestras, and heritage associations. The contributions to this volume explore the intersection of cultural heritage and nationality in societies that are characterized by national, multi-national, and post-national concepts. They question the roles that cultural heritage plays in its various contexts, and the ways in which ideology functions to produce it

Optimisation pour l'ordonnancement et le spatial

L’optimisation de processus complexes fait l’objet d’études en Recherche Opérationnelle et Optimisation Mathématique. Mes travaux en optimisation se sont concentrés sur deux types d’application : les problèmes d’ordonnancement et les problèmes issus du spatial. Parmi les problèmes d’ordonnancement, les problèmes cycliques correspondent à ceux pour lesquelles les tâches se répètent périodiquement. Ces problèmes ont été étudiés dans la littérature mais la plupart des travaux considèrent des paramètres déterministes. Pourtant, des incertitudes, comme la durée d’execution des tâches, peuvent survenir. Mes travaux sur l’ordonnancement cyclique visent à considérer ces incertitudes sous la forme d’un problème d'optimisation robuste bi-niveau. Une méthode de résolution basée sur une décomposition de Benders pour la version flexible du problème d'ordonnancement cyclique constitue une autre contribution dans ce domaine. Concernant les problématiques du spatial, les technologies modernes posent de nouveaux problèmes d’optimisation que nous tentons de résoudre tels que l’optimisation du placement de faisceau d’un satellite de télécommunication. Pour résoudre ce problème, nous proposons un encadrement paramétrable de la norme euclidienne dans le plan

Sublinear Algorithm And Lower Bound For Combinatorial Problems

As the scale of the problems we want to solve in real life becomes larger, the input sizes of the problems we want to solve could be much larger than the memory of a single computer. In these cases, the classical algorithms may no longer be feasible options, even when they run in linear time and linear space, as the input size is too large. In this thesis, we study various combinatorial problems in different computation models that process large input sizes using limited resources. In particular, we consider the query model, streaming model, and massively parallel computation model. In addition, we also study the tradeoffs between the adaptivity and performance of algorithms in these models.We first consider two graph problems, vertex coloring problem and metric traveling salesman problem (TSP). The main results are structure results for these problems, which give frameworks for achieving sublinear algorithms of these problems in different models. We also show that the sublinear algorithms for (∆ + 1)-coloring problem are tight. We then consider the graph sparsification problem, which is an important technique for designing sublinear algorithms. We give proof of the existence of a linear size hypergraph cut sparsifier, along with a polynomial algorithm that calculates one. We also consider sublinear algorithms for this problem in the streaming and query models. Finally, we study the round complexity of submodular function minimization (SFM). In particular, we give a polynomial lower bound on the number of rounds we need to compute s − t max flow - a special case of SFM - in the streaming model. We also prove a polynomial lower bound on the number of rounds we need to solve the general SFM problem in polynomial queries