Time-Space Trade-Off for Finding the k-Visibility Region of a Point in a Polygon

Bahoo, Yeganeh; Banyassady, Bahareh; Bose, Prosenjit; Durocher, Stéphane; Mulzer, Wolfgang

doi:10.1007/978-3-319-53925-6_24

Cited by 7 publications

(5 citation statements)

References 12 publications

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“…Given V, we can compute EMST(V) in O(n log n) time using O(n) words of workspace [11]. Given n sites in the plane, their EMST is the minimum spanning tree with the sites as vertices, where the weight of the edge between two sites is their Euclidean distance [12,13,14].…”

Section: Mathematical Formulationmentioning

confidence: 99%

Simultaneous Optimization of Electrical Interconnection Configuration in Onshore Wind Fields

Celeska

Krkoleva

Najdenkoski

et al. 2019

JEEIT

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The electrical interconnection cost of onshore wind fields (WF) is a part that should not be neglected in the design of WF. In order to minimize the investment and operational costs, this paper proposes an optimization formulation to find the optimal electrical interconnection configuration of wind turbines (WTs), simultaneously. This simultaneous minimization of total trenching length is done during а WF layout optimization by application of evolutional algorithm. In this paper, an algorithm is considered to comprehensively assess the optimal interconnection layout of the WTs. The interconnections are considerable fraction of the overall design cost of the WF. The optimal electrical interconnection design obtained by an algorithm with implemented Euclidean Minimum Spanning Tree method, corresponds to a lower cost and coupled with the technological developments can help policy makers and WF developers increase the use of onshore wind energy as a feasible unlimited renewable source of electrical energy.

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Section: Mathematical Formulationmentioning

confidence: 99%

Simultaneous Optimization of Electrical Interconnection Configuration in Onshore Wind Fields

Celeska

Krkoleva

Najdenkoski

et al. 2019

JEEIT

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show abstract

“…, e i+s−1 of E R . This can be done with a trick by Chan and Chen [12], similar to the procedure in the second algorithm in [7]. More precisely, whenever we produce new edges of RNG(V ), we store the edges that are longer than e i−1 in an array A of size O(s).…”

Section: The Algorithmmentioning

confidence: 99%

Time-Space Trade-Offs for Computing Euclidean Minimum Spanning Trees

Banyassady

Barba

Mulzer

2018

LATIN 2018: Theoretical Informatics

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In the limited-workspace model, we assume that the input of size n lies in a random access read-only memory. The output has to be reported sequentially, and it cannot be accessed or modified. In addition, there is a read-write workspace of O(s) words, where s ∈ {1, . . . , n} is a given parameter. In a time-space trade-off, we are interested in how the running time of an algorithm improves as s varies from 1 to n.We present a time-space trade-off for computing the Euclidean minimum spanning tree (EMST) of a set V of n sites in the plane. We present an algorithm that computes EMST(V ) using O(n 3 log s/s 2 ) time and O(s) words of workspace. Our algorithm uses the fact that EMST(V ) is a subgraph of the boundeddegree relative neighborhood graph of V , and applies Kruskal's MST algorithm on it. To achieve this with limited workspace, we introduce a compact representation of planar graphs, called an s-net which allows us to manipulate its component structure during the execution of the algorithm. * B.B. and W.M. were supported in part by DFG project MU/3501/2. L.B. was supported by the ETH Postdoctoral Fellowship.

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“…. , n}, Bahoo et al [16] provided a time-space trade-off that computes the k-visible region of p in a polygonal region P in O (k + c)n/s + n log s time using s cells of workspace, where s may range from 1 to n. Here, 1 ≤ c ≤ n is the number of "critical" vertices of P , i.e., vertices, where the k-visible region may change. 6 This algorithm makes use of known time-space trade-offs for the k-selection problem [31] and requires a careful analysis of the combinatorics of the k-visible region of p in P .…”

Section: Visibilitymentioning

confidence: 99%

Geometric Algorithms with Limited Workspace: A Survey

Banyassady,

Korman,

Mulzer

2018

Preprint

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In the limited workspace model, we consider algorithms whose input resides in read-only memory and that use only a constant or sublinear amount of writable memory to accomplish their task. We survey recent results in computational geometry that fall into this model and that strive to achieve the lowest possible running time. In addition to discussing the state of the art, we give some illustrative examples and mention open problems for further research.

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Time-Space Trade-Off for Finding the k-Visibility Region of a Point in a Polygon

Cited by 7 publications

References 12 publications

Simultaneous Optimization of Electrical Interconnection Configuration in Onshore Wind Fields

Simultaneous Optimization of Electrical Interconnection Configuration in Onshore Wind Fields

Time-Space Trade-Offs for Computing Euclidean Minimum Spanning Trees

Geometric Algorithms with Limited Workspace: A Survey

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