Covering points with minimum/maximum area orthogonally convex polygons

Evrendilek, Cem; Genç, Burkay; Hnich, Brahim

doi:10.1016/j.comgeo.2016.02.003

Cited by 2 publications

(3 citation statements)

References 8 publications

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“…It is easy to obtain polynomial time algorithms for the second problem when k = 1, since the solution consists of all points in the convex hull of S. The continuous version for d = k = 2 can be solved in O(n 4 log n) time [3]. Also, the orthogonal version of the problem is well studied (see for example [21]). We know of no results for the digital version.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Peeling Digital Potatoes

Crombez,

da Fonseca,

Gérard

2018

Preprint

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The potato-peeling problem (also known as convex skull) is a fundamental computational geometry problem that consist in finding the largest convex shape inside a given polygon. The fastest algorithm to date runs in O(n 8 ) time for a polygon with n vertices that may have holes. In this paper, we consider a digital version of the problem.where conv(K) denotes the convex hull of K. Given a set S of n lattice points, we present polynomial time algorithms for the problems of finding the largest digital convex subset K of S (digital potato-peeling problem) and the largest union of two digital convex subsets of S. The two algorithms take roughly O(n 3 ) and O(n 9 ) time, respectively. We also show that those algorithms provide an approximation to the continuous versions.

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Section: Conclusion and Open Problemsmentioning

confidence: 99%

Peeling Digital Potatoes

Crombez,

da Fonseca,

Gérard

2018

Preprint

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“…We study the minimal decompositions of rectilinear polygons into rectangles associated with the task of generating and propagating electromagnetic interference in multilayer printed circuit boards in [10]. Convex polygons of the minimum and maximum area are also considered in [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…The two other coordinates of the vertices of the triangle ∆ are as follows: ( Length of ∆ is equal to: E3S Web of Conferences 164, 02004 (2020) TPACEE-2019 https://doi.org/10.1051/e3sconf /So the area of ∆ may be written down like:Investigating ( , ) on extremums in the area ∈ (−∞; 0) ∈ (0; +∞). To do it let us study the derivatives of this function of two variables(13)…”

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confidence: 99%

Flat area characteristics of polygons circumscribing parabolic figures

2020

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The works elucidates the extremum areas of the polygons circumscribing parabolic figures. It is shown that the ratio of the areas of the polygons circumscribed near parabolic figures to the areas of the corresponding figures always remains a constant value, independent of the coefficients characterizing the quadratic function. The only point at which the function under study reaches its minimum value is found. The question of the necessary conditions for the existence of a circle circumscribed about a parabolic quadrilateral found in the Ptolemy theorem is being considered.

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Covering points with minimum/maximum area orthogonally convex polygons

Cited by 2 publications

References 8 publications

Peeling Digital Potatoes

Peeling Digital Potatoes

Flat area characteristics of polygons circumscribing parabolic figures

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