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 ...

We conduct a comprehensive review on multi-level facility location problems which extend several classical facility location problems and can be regarded as a subclass within the well-established field of hierarchical facility location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions in...

The objective of the study was to determine the spatial variation in modern contraceptive use and unmet need for family planning across the counties of Kenya and to examine whether the spatial patterns were associated with inequalities in physical access to health facilities. Data were obtained from the 2008-2009 Kenya Demographic and Health Survey and linked to the location of health facilitie...

With the rapid explosion of information based on location, spatial clustering plays an increasingly significant role in this day and age as an important technique in geographical data analysis. Most existing spatial clustering algorithms are limited by complicated spatial patterns, which have difficulty in discovering clusters with arbitrary shapes and uneven density. In order to overcome such ...

We analyze the polytope associated with a combinatorial problem that combines the Steiner tree problem and the uncapacitated facility location problem. The problem, called connected facility location problem, is motivated by a real-world application in the design of a telecommunication network, and concerns with deciding the facilities to open, the assignment of customers to open facilities, an...

In this paper we present a randomized constant factor approximation algorithm for the problem of computing the optimal cost of the metric Minimum Facility Location problem, in the case of uniform costs and uniform demands, and in which every point can open a facility. By exploiting the fact that we are approximating the optimal cost without computing an actual solution, we give the first algori...