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: A convex parimutuel call auction implemented at a central market organizer computer includes receiving orders from market participants, calculating a quantity of accepted bids for each of the orders, and communicating to the participants the calculated quantity of accepted bids for each of the orders. Each order includes a specification by a participant of contingent claims on outcomes of a future event, a limit bid price, and a limit bid quantity. The calculation involves maximizing an objective function given by an approximate profit to the market organizer plus a weighted logarithmic penalty function. Because the formulation is convex, the solution may be computed in polynomial time using standard techniques, such as a path-following algorithm.

Abstract: A convex paramutuel call auction implemented at a central market organizer computer includes receiving orders from market participants, calculating a quantity of accepted bids for each of the orders, and communicating to the participants the calculated quantity of accepted bids for each of the orders. Each order includes a specification by a participant of contingent claims on outcomes of a future event, a limit bid price, and a limit bid quantity. The calculation involves maximizing an objective function given by an approximate profit to the market organizer plus a weighted logarithmic penalty function. Because the formulation is convex, the solution may be computed in polynomial time using standard techniques, such as a path-following algorithm.

Abstract: The present invention uses a Semidefinite Programming (SDP) relaxation based method for the position estimation problem in sensor networks wherein the original problem is converted into a convex optimization problem. Estimation errors can be calculated, such that the quality of the solution to the initial problem is known. The sensor network may be divided into clusters such that the position estimation problem and the computation work can be distributed. The distributed scheme is highly scalable. A network with thousands of sensors may be solved within several minutes.

Abstract: The present invention uses a Semidefinite Programming (SDP) relaxation based method for the position estimation problem in sensor networks wherein the original problem is converted into a convex optimization problem. Estimation errors can be calculated, such that the quality of the solution to the initial problem is known. The sensor network may be divided into clusters such that the position estimation problem and the computation work can be distributed. The distributed scheme is highly scalable. A network with thousands of sensors may be solved within several minutes.