Abstract: A computer system for allocating and routing a plurality of servicing objects within a map of a region such that work load is balanced across the plurality of servicing objects is provided. The system formulates a model for allocating and routing the plurality of servicing objects in the region. The model comprises a distance matrix based upon a first plurality of segments or a second plurality of intersections in the map. The memory stores instructions for partitioning the map into a plurality of disjoint contiguous sub-regions in view of the distance matrix using an equitable convex region partition algorithm. The memory further stores instructions for calculating a corresponding tour graph for each sub-region in the plurality of sub-regions, where, for each respective sub-region in the plurality of sub-regions, a servicing object in the plurality of servicing objects is assigned to the tour graph that corresponds to the respective sub-region.

Abstract: A computer system for allocating and routing a plurality of servicing objects within a map of a region such that work load is balanced across the plurality of servicing objects is provided. The system formulates a model for allocating and routing the plurality of servicing objects in the region. The model comprises a distance matrix based upon a first plurality of segments or a second plurality of intersections in the map. The memory stores instructions for partitioning the map into a plurality of disjoint contiguous sub-regions in view of the distance matrix using an equitable convex region partition algorithm. The memory further stores instructions for calculating a corresponding tour graph for each sub-region in the plurality of sub-regions, where, for each respective sub-region in the plurality of sub-regions, a servicing object in the plurality of servicing objects is assigned to the tour graph that corresponds to the respective sub-region.

Abstract: Adaptive rule-based methods to solve localization problems for ad hoc wireless sensor networks are disclosed. A large problem may be solved as a sequence of very small subproblems, each of which is solved by semidefinite programming relaxation of a geometric optimization model. The subproblems may be generated according to a set of sensor/anchor selection rules and a priority list. The methods scale well and provide improved positioning accuracy. A dynamic version may be used for estimating moving sensors locations in a real-time environment. The method may use dynamic distance measurement updates among sensors, and utilizes subproblem solving for static sensor localization. Methods to deploy sensor localization algorithms in clustered distributed environments are also provided, permitting application to arbitrarily large networks. In addition, the methods may be used to solve sensor localizations in 2D or 3D space. A preprocessor may be used for localization of networks without absolute position information.