Polygon scheduling

Consider a set of circles of the same length and r irregular polygons with vertices on a circle of this length. Each of the polygons has to be arranged on a given subset of all circles and the positions of the polygon on the different circles are depending on each other. How should the polygons be arranged relative to each other to minimize some criterion function depending on the distances between adjacent vertices on all circles? A decomposition of the set of all arrangements of the polygons into local regions in which the optimization problem is convex is given. An exact description of the local regions and a sharp bound on the number of local regions are derived. For the criterion functions minimizing the maximum weighted distance, maximizing the minimum weighted distance, and minimizing the sum of weighted distances the local optimization problems can be reduced to polynomially solvable network flow problems

Cyclic schedules for r irregularly occurring event

Consider r irregular polygons with vertices on some circle. Authors explains how the polygons should be arranged to minimize some criterion function depending on the distances between adjacent vertices. A solution of this problem is given. It is based on a decomposition of the set of all schedules into local regions in which the optimization problem is convex. For the criterion functions minimize the maximum distance and maximize the minimum distance the local optimization problems are related to network flow problems which can be solved efficiently. If the sum of squared distances is to be minimized a locally optimal solution can be found by solving a system of linear equations. For fixed r the global problem is polynomially solvable for all the above-mentioned objective functions. In the general case, however, the global problem is NP-hard

Power adjustment and scheduling in OFDMA femtocell networks

Densely-deployed femtocell networks are used to enhance wireless coverage in public spaces like office buildings, subways, and academic buildings. These networks can increase throughput for users, but edge users can suffer from co-channel interference, leading to service outages. This paper introduces a distributed algorithm for network configuration, called Radius Reduction and Scheduling (RRS), to improve the performance and fairness of the network. RRS determines cell sizes using a Voronoi-Laguerre framework, then schedules users using a scheduling algorithm that includes vacancy requests to increase fairness in dense femtocell networks. We prove that our algorithm always terminate in a finite time, producing a configuration that guarantees user or area coverage. Simulation results show a decrease in outage probability of up to 50%, as well as an increase in Jain's fairness index of almost 200%