Constrained Geodesic Centers of a Simple Polygon

For any two points in a simple polygon P, the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regions. In this paper, we show how to compute the geodesic centers constrained to a set of line segments or simple polygonal regions contained in P. Our results provide substantial improvements over previous algorithms

Covering Points by Disjoint Boxes with Outliers

For a set of n points in the plane, we consider the axis--aligned (p,k)-Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain n-k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have O(n+k log k) time for p=1, and O(n log n+k^p log^p k time for p = 2,3. For rectangles we get O(n + k^3) for p = 1 and O(n log n+k^{2+p} log^{p-1} k) time for p = 2,3. In all cases, our algorithms use O(n) space.Comment: updated version: - changed problem from 'cover exactly n-k points' to 'cover at least n-k points' to avoid having non-feasible solutions. Results are unchanged. - added Proof to Lemma 11, clarified some sections - corrected typos and small errors - updated affiliations of two author

Development and evaluation of open-source IEEE 1547.1 test scripts for improved solar integration

Distributed Energy Resources (DERs) equipped with standardized, interoperable, grid-support functionality have the capability to provide a range of services for power system operators. These requirements have been recently codified in the 2018 revision of the American DER interconnection and interoperability standard, IEEE Std. 1547, as well as the revised Canadian interconnection standard, CSA C22.3 No. 9. Currently, the IEEE standards committee is drafting a new revision of the IEEE Std. 1547.1 test standard, which outlines the test procedures for certifying equipment compliant to IEEE Std. 1547. In addition, it is often referenced as a test standard in CSA C22.3 No. 9. This draft test standard has not been fully exercised yet to identify mistakes, redundancies, and/or implementation challenges. In this work, an international community of research laboratories developed open-source IEEE Std. 1547.1 test scripts. The scripts are used to evaluate grid-support functions – such as constant-power-factor, volt-var, volt-watt, and frequency-watt functions – of several DER devices to the draft standard, EEE1547.1. Sample test results are presented and discussed, and recommendations are offered to improve the draft standard during the balloting process

Geometric matching algorithms for two realistic terrains

We consider a geometric matching of two realistic terrains, each of which is modeled as a piecewise-linear bivariate function. For two realistic terrains f and g where the domain of g is relatively larger than that of f, we seek to find a translated copy f' of f such that the domain of f' is a sub-domain of g and the L-infinity or the L-1 distance of f' and g restricted to the domain of f' is minimized. In this paper, we show a tight bound on the number of different combinatorial structures that f and g can have under translation in their projections on the xy-plane. We give a deterministic algorithm and a randomized one that compute an optimal translation of f with respect to g under L-infinity metric. We also give a deterministic algorithm that computes an optimal translation of f with respect to g under L-1 metric. (C) 2018 Elsevier B.V. All rights reserved.110sciescopu

Spatial Skyline Queries: An Efficient Geometric Algorithm

As more data-intensive applications emerge, advanced retrieval semantics, such as ranking and skylines, have attracted attention. Geographic information systems are such an application with massive spatial data. Our goal is to efficiently support skyline queries over massive spatial data. To achieve this goal, we first observe that the best known algorithm VS(2), despite its claim, may fail to deliver correct results. In contrast, we present a simple and efficient algorithm that computes the correct results. To validate the effectiveness and efficiency of our algorithm, we provide an extensive empirical comparison of our algorithm and VS(2) in several aspects.1111sciescopu

Computing k-center over streaming data for small k

The Euclidean k-center problem is to compute k congruent balls covering a given set of points in Rd such that the radius is minimized. We consider the k-center problem in R-d for k = 2,3 in a single-pass streaming model, where data is allowed to be examined once and only a small amount of information can be stored in a device. We present two approximation algorithms whose space complexity does not depend on the size of the input data. The first algorithm guarantees a (2+epsilon)-factor using O(d/epsilon) space in arbitrary dimensions, and the second algorithm guarantees a (1+epsilon)-factor using O(1/epsilon(d)) space in constant dimensions. The same algorithms can be used to compute a k-center under any L-p metric for k = 2, 3.111sciescopu

Digital Twin for Operation of Microgrid: Optimal Scheduling in Virtual Space of Digital Twin

Due to the recent development of information and communication technology (ICT), various studies using real-time data are now being conducted. The microgrid research field is also evolving to enable intelligent operation of energy management through digitalization. Problems occur when operating the actual microgrid, causing issues such as difficulty in decision making and system abnormalities. Using digital twin technology, which is one of the technologies representing the fourth industrial revolution, it is possible to overcome these problems by changing the microgrid configuration and operating algorithms of virtual space in various ways and testing them in real time. In this study, we proposed an energy storage system (ESS) operation scheduling model to be applied to virtual space when constructing a microgrid using digital twin technology. An ESS optimal charging/discharging scheduling was established to minimize electricity bills and was implemented using supervised learning techniques such as the decision tree, NARX, and MARS models instead of existing optimization techniques. NARX and decision trees are machine learning techniques. MARS is a nonparametric regression model, and its application has been increasing. Its performance was analyzed by deriving performance evaluation indicators for each model. Using the proposed model, it was found in a case study that the amount of electricity bill savings when operating the ESS is greater than that incurred in the actual ESS operation. The suitability of the model was evaluated by a comparative analysis with the optimization-based ESS charging/discharging scheduling pattern

Square and rectangle covering with outliers

info:eu-repo/semantics/publishe

Square and Rectangle Covering with Outliers

For a set of n points in the plane, we consider the axis-aligned (p; k)-Box COVERING problem: Find p axis-aligned, pairwise disjoint. boxes that together contain exactly n-k points. Here, our boxes are either squares or rectangles, and we want to minimize the area of the largest box. For squares, we present algorithms that find the solution in O(n + k log k) time for p = 1. and in O(n log n + k(p) log(p) k) time for p = 2; 3. For rectangles we have running times of O(n + k(3)) for p = 1 and O(n log n + k(2+p) log(p-1) k) time for p = 2; 3. In all cases; our algorithms use O(n) space.11sciescopu

Square and rectangle covering with outliers

Proceedings of the 3rd Frontiers of Algorithmics Workshop (FAW’09)info:eu-repo/semantics/publishe