Equitable partitioning with obstacles
نویسندگان
چکیده
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, represented by a set of n fixed points in the territory. We give a fast analytic center cutting plane method that divides the territory into n compact, connected sub-regions, each of which contains a facility, such that the workloads in each sub-region are “balanced”. Our approach can also be used to design a control policy that allows us to design the sub-regions in a decentralized fashion.
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