The study of the facility location problem in the presence of self-interested agents has recently emerged as the benchmark problem in the research on mechanism design without money. In the setting studied in the literature so far, agents are single-parameter in that their type is a single number encoding their position on a real line. We here initiate a more realistic model for several real-lif...

In this paper we apply theoretical and practical results from facility location theory to the problem of community detection in networks. The result is an algorithm that computes bounds on a minimization variant of local modularity. We also define the concept of an edge support and a new measure of the goodness of community structures with respect to this concept. We present preliminary results...

In this study, we consider facility location decisions for a humanitarian relief chain responding to quick-onset disasters. In particular, we develop a model that determines the number and locations of distribution centres in a relief network and the amount of relief supplies to be stocked at each distribution centre to meet the needs of people affected by the disasters. Our model, which is a v...

1.2 Hardness of k-median Theorem 1. It is hard to approximate k-median within 1+ 2 e1/c for any c < 1. This theorem is equivalent to the 1− 1/e− hardness shown in [2] and follows from a standard reduction from set cover. The main idea is to take an approximation algorithm for k-median, and use it to obtain a partial set cover. Then repeat this process, again partially covering the remaining ite...

We study the problem of locating a public facility on a real line or an interval, when agents’ costs are their (expected) distances from the location of the facility. Our goal is to minimize the maximum envy over all agents, which we will refer to as the minimax envy objective, while at the same time ensuring that agents will report their most preferred locations truthfully. First, for the prob...

Jain et al. proposed two well-known algorithms for the Metric Facility Location Problem (MFLP), that achieve approximation ratios of 1.861 and 1.61. Mahdian et al. combined the latter algorithm with scaling and greedy augmentation techniques, obtaining a 1.52-approximation for the MFLP. We consider a generalization of the Squared Euclidean Facility Location Problem, when the distance function i...

In this paper we define the multi-commodity connected facility location (MCFL) problem, a natural generalization of the well-known multi-commodity rent-or-buy (MROB) and connected facility location (CFL) network design problems. Like in MROB, we wish to send one unit of flow from a set of sources to a set of sinks. This flow is supported by renting or buying edges. For each bought edge e, we pa...

This thesis is in Computational Geometry. Computational Geometry is a subfield of Computer Science that deals with problems of a geometric nature that arise in application domains such as Computer Graphics, Robotics, Geographic Information Systems (GIS), and Molecular Biology. More specifically, in this thesis we conduct research in Computational Geometry in the context of (Geometric) Facility ...