In the Nearest Neighbor problem (NN), the objects in the database that are nearer to a given query object than any other objects in the database have to be found. In the conceptually inverse problem, Reverse Nearest Neighbor problem (RNN), objects that have the query object as their nearest neighbor have to be found. Reverse Nearest Neighbors queries have emerged as an important class of querie...

We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized onlineO(1)-competitive algorithm in the case where points arrive in random order. If points are ordered adversarially, we show that no algorithm can be constant-competitive, and provide an O(logn)-competitive a...

In the Universal Facility Location problem we are given a set of demand points and a set of facilities. The goal is to assign the demands to facilities in such a way that the sum of service and facility costs is minimized. The service cost is proportional to the distance each unit of demand has to travel to its assigned facility, whereas the facility cost of each facility i depends on the amoun...

Facility location games have been a topic of major interest in economics, operations research and computer science, starting from the seminal work by Hotelling. Spatial facility location models have successfully predicted the outcome of competition in a variety of scenarios. In a typical facility location game, users/customers/voters are mapped to a metric space representing their preferences, ...

In out last lecture, we discussed the LP Rounding technique for producing approximation algorithms. The idea behind LP Rounding is to write the problem as an integer linear program, relax its integrality restraints to efficiently solve the general linear program, and then move the LP solution to a nearby integral point in the feasible solution space. The difficulty of this process lies in the r...

proposing a robust designed facility location is one of the most effective ways to hedge against unexpected disruptions and failures in a transportation network system. this paper considers the combined facility location/network design problem with regard to transportation link disruptions and develops a mixed integer linear programming formulation to model it. with respect to the probability o...

The facility location problem has occupied a central place in operations research since the early 1960's, as it models design decisions on the placement of factories, warehouses, schools, or hospitals to serve a set of customers efficiently. For an overview of previous work see the survey chapter by Cornue-jols, Nemhauser & Wolsey in [21]. Recently, it has received renewed research interest bec...

Let A be a nonempty nite subset of the plane representing the geographical coordinates of a set of demand points (towns,. . .), to be served by a facility, whose location within a given region S is sought. Assuming that the unit cost for a 2 A if the facility is located at x 2 S is proportional to dist(x; a) | the distance from x to a | and that demand of point a is given by ! a , minimizing th...

Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers. Motivated by these platforms, we formulate a set of facility location problems that we term Two-sided Facility location. In our model, agents arrive at nodes in an ...

Dr. Christoph Witzgall, the honoree of this Symposium, can count among his many contributions to applied mathematics and mathematical operations research a body of widely-recognized work on the optimal location of facilities. The present paper offers to non-specialists a sketch of that field and its evolution, with emphasis on areas most closely related to Witzgall's research at NBS/NIST.