Dynamic Minimum Bichromatic Separating Circle

Armaselu, Bogdan; Daescu, Ovidiu

doi:10.1007/978-3-319-26626-8_50

Cited by 2 publications

(8 citation statements)

References 6 publications

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“…First, we improve upon the MBSR-O result in [3]. Specifically, we provide a slight improvement of O(k 7 m + m log m + n) time for k outliers, which we further improve to O(k 3 m + km log m + n) time.…”

Section: Our Resultsmentioning

confidence: 90%

“…However, there are also results for blue obstacles. In a more recent paper [3], Armaselu, Daescu, Fan, and Raichel give an algorithm to find a largest rectangle separating red points from blue axis-aligned rectangles in O(m log m + n) time.…”

Section: Related Workmentioning

confidence: 99%

“…In this paper, we consider two extensions of the MBSR problem. The first extension, introduced in [3], is called MBSR with outliers (MBSR-O) or simply outliers version. It seeks to find the largest axis-aligned rectangle containing all red points and up to k blue points outside S min , where k is given as part of the input.…”

Section: Introductionmentioning

confidence: 99%

“…That is, MBSR-O is a relaxation of condition (2) from the original MBSR problem. The running time of the algorithm in [3] is O(k 7 mlogm + n). However, when the k is large (e.g., k = Θ(m)), this running time bound can be unreasonably high.…”

Section: Introductionmentioning

confidence: 99%

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Extensions of the Maximum Bichromatic Separating Rectangle Problem

Armaselu

2022

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An important topic in the field of geometric optimization is finding the largest rectangle separating two different points sets, which has significant applications in circuit design and data science. We consider some extensions of the maximum bichromatic separating rectangle (MBSR) problem. In one of the extensions, the optimal rectangle may include up to k outliers, where k is given as part of the input. This extension and is called MBSR with outliers or MBSR-O. In this paper, we improve the current known time bounds for MBSR-O from O(k7mlogm+n) to O(k3m+kmlogm+n) using a clever staircase sweep approach. We also propose another extension, which is named MBSR among circles or MBSR-C and asks for the largest rectangle separating red points from blue unit circles. Our solution to MBSR-C is an O(m2+n)-time algorithm that involves an optimized scanning of all candidate circle arcs for locations of potential optimal solutions.

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Section: Our Resultsmentioning

confidence: 90%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extensions of the Maximum Bichromatic Separating Rectangle Problem

Armaselu

2022

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“…In 1975, an algorithm with time order O (nlogn) was proposed to solve this problem and then proceeded to optimum time O (n), with the help of a linear programming method [7] . The problem is to find the smallest rectangle parallel to the x-axis, which covers exactly n points of P, and solved by the agraval [8] at time O(k 2 nlogn), Epstein [9] at time O(n 2 ) and Segal M. and Kedem K. [7] At time O(n+k (n-k) 2 ).…”

Section: Research Backgroundmentioning

confidence: 99%

Designing a metaheuristic mining algorithm to separate two-color points in a two-dimensional environment

2019

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The separation of color points is one of the important issues in computational geometry, which is used in various parts of science; it can be used in facility locating, image processing and clustering. Among these, one of the most widely used computational geometry in the real-world is the problem of covering and separating points with rectangles. In this paper, we intend to consider the problemof separating the two-color points sets, using three rectangles. In fact, our goal is to separate desired blue points from undesired red points by three rectangles, in such a way that these three rectangles contain the most desire points. For this purpose, we provide a metaheuristic algorithm based on the simulated annealing method that could separates blue points from input points, , in time order O (n) with the help of three rectangles. The algorithm is executed with C# and also it has been compared and evaluated with the optimum algorithm results. The results show that our recommended algorithm responses is so close to optimal responses, and also in some cases we obtains the exact optimal response.

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Dynamic Minimum Bichromatic Separating Circle

Cited by 2 publications

References 6 publications

Extensions of the Maximum Bichromatic Separating Rectangle Problem

Extensions of the Maximum Bichromatic Separating Rectangle Problem

Designing a metaheuristic mining algorithm to separate two-color points in a two-dimensional environment

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