We present fast approximation algorithms for the problem of dividing a given convex geographic region into smaller sub-regions so as to distribute the workloads of a set of vehicles. Our objective is to partition the region in such a fashion as to ensure that vehicles are capable of communicating with one another under limited communication radii. We consider variations of this problem in which sub-regions are constrained to have equal area or be convex, and as a side consequence, our approach yields a factor 1.99 approximation algorithm for the continuous k-centers problem on a convex polygon.
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The authors gratefully acknowledge DARPA Young Faculty Award N66001-12-1-4218, NSF Grant CMMI-1234585, and ONR Grant N000141210719.
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Carlsson, J.G., Behroozi, M. & Li, X. Geometric partitioning and robust ad-hoc network design. Ann Oper Res 238, 41–68 (2016). https://doi.org/10.1007/s10479-015-2093-0
- Geometric partitioning
- Network design
- Location set covering
- Vehicle routing
- approximation algorithms