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Let S be a set S of n points on a polyhedral terrain T in R3, and let ϵ > 0 be a fixed constant. We prove that S admits a (2 + ϵ)-spanner with O(n log n) edges with respect to the geodesic distance. This is the first spanner with constant spanning ratio and a near-linear number of edges for points on a terrain. On our way to this result, we prove that any set of n weighted points in Rd admits an additively weighted (2 + ϵ)-spanner with O(n) edges; this improves the previously best known bound on the spanning ratio (which was 5 + ϵ), and almost matches the lower bound. Copyright © by SIAM  

Let S be a set of n points on a polyhedral terrain T in ℝ3, and let ϵ > 0 be a fixed constant. We prove that S admits a (2 + ϵ )-spanner with O(n log n) edges with respect to the geodesic distance. This is the first spanner with constant spanning ratio and a near-linear number of edges for points on a terrain. On our way to this result, we prove that any set of n weighted points in Rd admits an additively weighted (2 + ϵ )-spanner with O(n) edges; this improves the previously best known bound on the spanning ratio (which was 5 + ϵ ) and almost matches the lower bound. © 2019 Society for Industrial and Applied Mathematics Publications. All rights reserved  

Let S be a set of n points on a polyhedral terrain T in ℝ3, and let ϵ > 0 be a fixed constant. We prove that S admits a (2 + ϵ )-spanner with O(n log n) edges with respect to the geodesic distance. This is the first spanner with constant spanning ratio and a near-linear number of edges for points on a terrain. On our way to this result, we prove that any set of n weighted points in Rd admits an additively weighted (2 + ϵ )-spanner with O(n) edges; this improves the previously best known bound on the spanning ratio (which was 5 + ϵ ) and almost matches the lower bound. © 2019 Society for Industrial and Applied Mathematics Publications. All rights reserved  

Let P be a set of n points in R3 amid a bounded number of obstacles. Consider the metric space M=(P,dM) where dM(p,q) is the geodesic distance of p and q, i.e., the length of a shortest path from p to q avoiding obstacles. When obstacles are axis-parallel boxes, we prove that M admits an 83-spanner with O(nlog3⁡n) edges. In other words, let S be a complete graph on n vertices where each node corresponds to a point p∈P. For nodes u and v of S corresponding to p,q∈P, the edge (u,v) is associated with the geodesic distance of p and q as its weight. We indeed prove that S admits a near linear-size t-spanner for some constant t. © 2020 Elsevier B.V  

Let P be a set of n points in R3 amid a bounded number of obstacles. Consider the metric space M=(P,dM) where dM(p,q) is the geodesic distance of p and q, i.e., the length of a shortest path from p to q avoiding obstacles. When obstacles are axis-parallel boxes, we prove that M admits an 83-spanner with O(nlog3⁡n) edges. In other words, let S be a complete graph on n vertices where each node corresponds to a point p∈P. For nodes u and v of S corresponding to p,q∈P, the edge (u,v) is associated with the geodesic distance of p and q as its weight. We indeed prove that S admits a near linear-size t-spanner for some constant t. © 2020 Elsevier B.V  

Let (Formula presented.) be a set of n points inside a polygonal domain (Formula presented.). A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set (Formula presented.) with respect to the geodesic distance function (Formula presented.) where for any two points p and q, (Formula presented.) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., (Formula presented.)), we construct a ((Formula presented.))-spanner that has (Formula presented.)... 

Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function π where for any two points p and q, π(p, q) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., h= 0), we construct a (10+ϵ)-spanner that has O(nlog 2n) edges. For a case where there are h holes, our construction gives a (5 + ϵ)-spanner with the size of O(nhlog2n). Moreover, we study... 

Satellite-based navigation has rapidly evolved into an efficient tool extensively used in a wide variety of civilian applications covering numerous modes of transportation, communication, administration, geodesy, agriculture, etc. The current systems globally available are the US Global Positioning System (GPS) and the conceptually very similar Russian Global Navigation Satellite System (GLONASS). The European Union (EU) has also decided to press ahead with plans to develop Galileo system, a European version of the Global Positioning System (GPS) after the system definition during 1999/2000. The development phase of Galileo is expected to run from 2002 to 2005 with a deployment phase,... 

Online voltage security assessment is necessary to choose appropriate remedial and corrective actions in order to prevent a large-scale blackout. This paper presents a new online voltage security assessment method based on wide-area measurements and decision-tree algorithm. For the predicted load and generation variation scenarios (i.e., a day ahead), the database is obtained using continuation power flow. Moreover, each operating point is labeled as 'secure' or 'insecure' from voltage stability points of view based on WECC voltage security criteria. Decision trees are trained on the subset of the existing data by applying two famous splitting rules and various predictors. Bagging and... 

Semi-supervised learning based on manifolds has been the focus of extensive research in recent years. Convenient neighbourhood graph construction is a key component of a successful semi-supervised classification method. Previous graph construction methods fail when there are pairs of data points that have small Euclidean distance, but are far apart over the manifold. To overcome this problem, we start with an arbitrary neighbourhood graph and iteratively update the edge weights by using the estimates of the geodesic distances between points. Moreover, we provide theoretical bounds on the values of estimated geodesic distances. Experimental results on real-world data show significant... 

Power system restoration is the procedure of restoring a power system after a blackout and different strategies have developed for it because of its importance. One of the most practical and economical strategies is a "Build-up strategy" that includes the process of restoring separated islands in the power system and interconnecting them after it. The process of Build-up power system restoration is highly affected by power system telecommunication capabilities. Based on the constraints of wide area measurement system (WAMS) operation, each island must be fully observable. This paper provides an approach for power system restoration and observability of these islands. The New England 39 bus... 

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic distances, the low-dimensional embedding is computed via a path-mapping algorithm. Due to the much fewer number of paths compared to number of data points, a significant improvement in time and memory... 

This paper proposes a transient stability constrained controlled islanding (TSC-CI) approach against cascading events in power systems. Using the wide area measurements, the proposed islanding algorithm is implemented regarding the actual dynamic conditions of the resulted islands. Since the main concern, right after the execution of controlled network splitting, is the transient stability of synchronous machines, a transient energy function is utilized for proper network partitioning. The proposed transient stability criterion is expressed as a function of the transfer impedance between each pair of generators in the resulted islands. Transfer impedance between each pair of coherent... 

Monitoring/control infrastructures are often assumed to be fully reliable in power system reliability studies. However, recent investigations on blackouts have revealed the crucial impacts of monitoring/control system malfunctions. This paper addresses the impact of situational awareness and controllability on power system reliability assessment. A methodology is proposed to simulate a situation in which a limitation of either or both monitoring and control functions could spread the consequence of power system events throughout the grid. It is assumed that the monitoring/control infrastructure is based on a wide-area measurement system (WAMS). While the proposed methodology is applicable to... 

This paper enhances the observability of power networks by taking into consideration random component outages. The architecture of wide-area measurement system (WAMS) is analyzed in order to identify components that would affect the network observability. An iterative framework is devised to calculate a bus index in power networks equipped with phasor measurement units (PMUs) and conventional measurements. The average of bus indices represents a system index which provides an overall insight on the power network observability. The system index is utilized as a criterion to distinguish among multiple optimal PMU placements. Conventional bus injection and line flow measurements and the effect... 

Monitoring/control infrastructures are often assumed to be fully reliable in power system reliability studies. However, recent investigations on blackouts have revealed the crucial impacts of monitoring/control system malfunctions. This paper addresses the impact of situational awareness and controllability on power system reliability assessment. A methodology is proposed to simulate a situation in which a limitation of either or both monitoring and control functions could spread the consequence of power system events throughout the grid. It is assumed that the monitoring/control infrastructure is based on a wide-area measurement system (WAMS). While the proposed methodology is applicable to... 

Frequency control during power system restoration has not been strongly addressed. Operators are often concerned with the offline sizing of load and generation steps, but, nowadays, the introduction of Wide Area Measurement System (WAMS) makes it possible to monitor the stability of power system online. The constraints of WAMS operation result in some changes in power system frequency control. This paper proposes a novel methodology for frequency control and monitoring during the early steps of power system restoration based on WAMS. Detailed load modeling is achieved based on the static load modeling approach. Power generators' modeling is also accomplished utilizing the single machine... 

This paper enhances the observability of power networks by taking into consideration random component outages. The architecture of wide-area measurement system (WAMS) is analyzed in order to identify components that would affect the network observability. An iterative framework is devised to calculate a bus index in power networks equipped with phasor measurement units (PMUs) and conventional measurements. The average of bus indices represents a system index which provides an overall insight on the power network observability. The system index is utilized as a criterion to distinguish among multiple optimal PMU placements. Conventional bus injection and line flow measurements and the effect... 

One of important subjects in power system restoration that already is not addressed is frequency control. Operators are often concerned with the size of load and generation, which can be safely increased. With the emphasis on higher utilization of power systems, monitoring of its dynamics is becoming increasingly important. This requires information with higher accuracy and update rates faster than those usually provided by traditional SCADA systems. In addition, it must be synchronized over a wider geographical area than that provided by traditional protection systems. Nowadays, the introduction of Phasor Measurement Units (PMU) and Wide Area Monitoring Systems (WAMS) as well as advances in...