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We consider a geographic optimization problem in which we are given a region R, a probability density function f (·) defined on R, and a collection of n utility density functions ui(·) defined on R. Our objective is to divide R into n sub-regions Ri so as to " balance " the overall utilities on the regions, which are given by the integrals˜R i f (x)ui(x)… (More)

— Autonomous vehicles (or drones) are very frequently used for servicing a geographic region in numerous applications. Given a geographic territory and a set of n fixed vehicle depots, we consider the problem of designing service districts so as to balance the workload of a collection of vehicles which service this region. We assume that the territory is a… (More)

We consider the problem of dividing a geographic region into sub-regions so as to minimize the maximum workload of a collection of facilities over that region. We assume that the cost of servicing a demand point is a monomial function of the distance to its assigned facility and that demand points follow a continuous probability density. We show that, when… (More)

We consider the problem of dividing a territory into sub-regions so as to balance the workloads of a collection of facilities or vehicles over that territory. We assume that the territory is a connected polygonal region, i.e. a simply connected polygon containing a set of simply connected obstacles. The territory also contains a collection of facilities,… (More)

One of the fundamental concerns in the analysis of logistical systems is the trade-off between localized, independent provision of goods and services versus provision along a centralized infrastructure such as a backbone network. One phenomenon in which this trade-off has recently been made manifest is the transition of businesses from traditional… (More)

Spatial partitions of an information space are frequently used for data visualization. Weighted Voronoi diagrams are among the most popular ways of dividing a space into partitions. However, the problem of computing such a partition efficiently can be challenging. For example, a natural objective is to select the weights so as to force each Voronoi region… (More)

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