Finding Extremal Polygons

Boyce, James E.; Dobkin, David P.; Drysdale, Robert L. Scot; Guibas, Leo J.

doi:10.1137/0214011

Cited by 65 publications

(13 citation statements)

References 3 publications

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“…• We present a 9-vertex polygon on which the algorithm by Dobkin and Snyder for computing the largestarea triangle [1] fails. By extensions, the algorithm by Boyce et al and Aggarwal et al for computing the largest-area k-gon [11,12] also fail. In particular, the example disproves Lemma 2.5 of Dobkin and Snyder [1] and Lemma 3.2 of Boyce et al [11] (Section 7.2).…”

Section: Contributionmentioning

confidence: 99%

“…By extensions, the algorithm by Boyce et al and Aggarwal et al for computing the largest-area k-gon [11,12] also fail. In particular, the example disproves Lemma 2.5 of Dobkin and Snyder [1] and Lemma 3.2 of Boyce et al [11] (Section 7.2).…”

Section: Contributionmentioning

confidence: 99%

“…Our counter example is a polygon on 16 vertices in the range [0, 26500]. Our counter example, combined with the work in [10] and [11] would suggest that the problem of finding the largest-area quadrilateral in linear time is still open. Although Boyce et al [11] claimed one is presented by Shamos [7], but the cited manuscript cannot be found on-line.…”

Section: Introductionmentioning

confidence: 97%

“…Dobkin and Snyder [1] originally claimed to have a generic linear-time algorithm for finding the largest inscribed k-gon inside a convex polygon (for constant k), but this claim was later retracted: Boyce et al [11] observe that the algorithm by Dobkin and Snyder fails for k = 5 and instead present a O(kn log n + n log 2 n) algorithm for finding the largest k-gon. Aggarwal et al [12] improve their result to O(kn + n log n) time by using a matrix search method.…”

Section: Introductionmentioning

confidence: 99%

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Maximum-Area Triangle in a Convex Polygon, Revisited

Keikha,

Löffler,

Mohades

et al. 2017

Preprint

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We revisit the following problem: Given a convex polygon P , find the largest-area inscribed triangle. We show by example that the linear-time algorithm presented in 1979 by Dobkin and Snyder [1] for solving this problem fails. We then proceed to show that with a small adaptation, their approach does lead to a quadratic-time algorithm. We also present a more involved O(n log n) time divide-and-conquer algorithm. Also we show by example that the algorithm presented in 1979 by Dobkin and Snyder [1] for finding the largest-area k-gon that is inscribed in a convex polygon fails to find the optimal solution for k = 4. Finally, we discuss the implications of our discoveries on the literature.

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Section: Contributionmentioning

confidence: 99%

Section: Contributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Maximum-Area Triangle in a Convex Polygon, Revisited

Keikha,

Löffler,

Mohades

et al. 2017

Preprint

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“…Then, we compute three special polygons from the convex hull: the Largest Area Triangle and the Largest Area Quadrilateral inscribed in the convex hull [1], and finally, the Smallest Area Enclosing Rectangle [12].…”

Section: Geometry Extractionmentioning

confidence: 99%

Generic Shape Classification for Retrieval

Fonseca¹,

Ferreira²,

Jorge³

2006

Lecture Notes in Computer Science

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Abstract. We present a shape classification technique for structural content-based retrieval of two-dimensional vector drawings. Our method has two distinguishing features. For one, it relies on explicit hierarchical descriptions of drawing structure by means of spatial relationships and shape characterization. However, unlike other approaches which attempt rigid shape classification, our method relies on estimating the likeness of a given shape to a restricted set of simple forms. It yields for a given shape, a feature vector describing its geometric properties, which is invariant to scale, rotation and translation. This provides the advantage of being able to characterize arbitrary two-dimensional shapes with few restrictions. Moreover, our technique seemingly works well when compared to established methods for two dimensional shapes.

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An Improved Algorithm for the Traveler′s Problem

Aggarwal

Tokuyama

1995

Journal of Algorithms

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Finding Extremal Polygons

Cited by 65 publications

References 3 publications

Maximum-Area Triangle in a Convex Polygon, Revisited

Maximum-Area Triangle in a Convex Polygon, Revisited

Generic Shape Classification for Retrieval

An Improved Algorithm for the Traveler′s Problem

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