Closest Pair Algorithms in 2D space,a commentary on complexity and reductions

One of the most challenging problems in computational geometry is closest pair of points given n points. Brute force algorithms[1] and Divide and conquer[1] have been verified and the lowest complexity of attributed to latter class of algorithms, with worst case being for the former being . We propose a method of partitioning the set of n-points based on the least area rectangle that can circumscribe these points

An Appliance Scheduling System for Residential Energy Management

In this work, an Appliance Scheduling-based Residential Energy Management System (AS-REMS) for reducing electricity cost and avoiding peak demand while keeping user comfort is presented. In AS-REMS, based on the effects of starting times of appliances on user comfort and the user attendance during their operations, appliances are divided into two classes in terms of controllability: MC-controllable (allowed to be scheduled by the Main Controller) and user-controllable (allowed to be scheduled only by a user). Use of all appliances are monitored in the considered home for a while for recording users’ appliance usage preferences and habits on each day of the week. Then, for each MC-controllable appliance, preferred starting times are determined and prioritized according to the recorded user preferences on similar days. When scheduling, assigned priorities of starting times of these appliances are considered for maintaining user comfort, while the tariff rate is considered for reducing electricity cost. Moreover, expected power consumptions of user-controllable appliances corresponding to the recorded user habits and power consumptions of MC-controllable appliances corresponding to the assigned starting times are considered for avoiding peak demand. The corresponding scheduling problem is solved by Brute-Force Closest Pair method. AS-REMS reduces the peak demand levels by 45% and the electricity costs by 39.6%, while provides the highest level of user comfort by 88%. Thus, users’ appliance usage preferences are sustained at a lower cost while their comfort is kept impressively.