The Average Distance Between Two Points

Burgstaller, Bernhard; Pillichshammer, Friedrich

doi:10.1017/s0004972709000707

Cited by 40 publications

(23 citation statements)

References 8 publications

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“…In particular, using above formulae we obtain already known results for the mean distance between and when D is a disc, a regular triangle, a rectangle, a regular hexagon and a rhombus (see Santalo, 2004;Burgstaller, Pillichshammer, 2009;Dunbar, 1997).…”

Section: Introductionmentioning

confidence: 74%

“…В частности, используя явный вид для ( ), вычислены средние расстояния в случае, когда точки и случайно брошены в круг, в правильный треугольник, прямоугольник, в правильных шестиугольник и ромб (см. Santalo, 2004;Burgstaller, Pillichshammer, 2009;Dunbar, 1997).…”

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Moments of the Distance between Two Random Points

2016

Modeling of Artificial Intelligence

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Let be a bounded convex domain in the Euclidean plane and we choose uniformly and independently points and from Denote by ( ) the Euclidean distance between points and and by ( ) the distribution function of ( ). Using the explicit form of distribution function we obtain a formula for the calculation of moments of order for any natural . In particular, using the formula for ( ), we derive the mean distance between the points and for a disc, a regular triangle, a rectangle, a regular hexagon and a rhombus (see

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Section: Introductionmentioning

confidence: 74%

Section: удк 004unclassified

Moments of the Distance between Two Random Points

2016

Modeling of Artificial Intelligence

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“…for a constant A. From the average separation of a random pair of points within a sphere, which is 36/35 times the radius (Burgstaller and Pillichshammer, 2009) and 20…”

Section: Path Lengthmentioning

confidence: 99%

Effects of Parcellation and Threshold on Brain Connectivity Measures

Lacy

Robinson

2019

Preprint

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It is shown that the statistical properties of connections between regions of the brain and their dependence on coarse-graining and thresholding in published data can be reproduced by a simple distance-based physical connectivity model. This allows studies with differing parcellation and thresholding to be interrelated objectively, and for the results of future studies on more finely grained or differently thresholded networks to be predicted. The dependence of network measures on thresholding and parcellation implies that chosen brain regions can appear to form a small world network in many studies, even though the network of individual neurons may not be a small world network itself.

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“…We again interpret our fitness gain results in terms of the expected approximation ratio, similar to the previous analysis on Manhattan instances. Here, we refer to the previous study of Burgstaller and Pillichshammer [3] to derive the expected length of the initial tour.…”

Section: The Approximation Ratio Over the Algorithm Runmentioning

confidence: 99%

Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem

Nallaperuma

Neumann

Sudholt

2017

Evolutionary Computation

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Randomized search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to our theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed-time budget. We follow this approach and present a fixed-budget analysis for an NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson Problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve within a given fixed-time budget. In particular, we analyze Manhattan and Euclidean TSP instances and Randomized Local Search (RLS), (1+1) EA and (1+[Formula: see text]) EA algorithms for the TSP in a smoothed complexity setting, and derive the lower bounds of the expected fitness gain for a specified number of generations.

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The Average Distance Between Two Points

Abstract: We provide bounds on the average distance between two points uniformly and independently chosen from a compact convex subset of the s-dimensional Euclidean space.2000 Mathematics subject classification: primary 52A22; secondary 60D05.

Cited by 40 publications

References 8 publications

Moments of the Distance between Two Random Points

Moments of the Distance between Two Random Points

Effects of Parcellation and Threshold on Brain Connectivity Measures

Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem

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