scholarly journals Locality and bounding-box quality of two-dimensional space-filling curves

2010 ◽  
Vol 43 (2) ◽  
pp. 131-147 ◽  
Author(s):  
Herman Haverkort ◽  
Freek van Walderveen
Keyword(s):  
Dimensional Space ◽  
Two Dimensional ◽  
Space Filling ◽  
Space Filling Curves ◽  
Bounding Box

scholarly journals Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Ho-Kwok Dai ◽  
Hung-Chi Su
Keyword(s):  
Random Walk ◽  
Dimensional Space ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Order Curve ◽  
Cluster Distance ◽  
The Mean ◽  
Curve Family

International audience A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.

Exploration of a Mobile Robot Based on Sonar Probability Mapping

1996 ◽  
Vol 118 (1) ◽  
pp. 150-157
Author(s):  
Byung-Kwon Min ◽  
Dong Woo Cho ◽  
Sang-Jo Lee ◽  
Young-Pil Park
Keyword(s):  
Probability Theory ◽  
Mobile Robot ◽  
Dimensional Space ◽  
Bayesian Probability ◽  
Autonomous Mobile Robot ◽  
Two Dimensional ◽  
Probability Map ◽  
Work Area

This paper suggests a new exploration strategy of an autonomous mobile robot in an unknown environment. Determination of a temporary goal based on a representation of work area named exploration quadtree is proposed. The exploration quadtree provides the information on quality of the regions concerned in a robot’s workspace. Using this quadtree the robot easily finds the next temporary goal that makes exploration more efficient. The quadtree is made up from a sonar probability map that is constructed by sonar range sensing and Bayesian probability theory. We then propose a method that plans a path between the determined temporary goals based on a probability map. The developed methods were implemented on a real mobile robot, AMROYS-II, which was built in our laboratory, and shown to be useful enough in a real environment that can be projected onto a two-dimensional space.

Visualizing Evolutionary Activity of Genotypes

1999 ◽  
Vol 5 (1) ◽  
pp. 17-35 ◽  
Author(s):  
Mark A. Bedau ◽  
C. Titus Brown
Keyword(s):  
Competitive Exclusion ◽  
Dimensional Space ◽  
Assembly Language ◽  
Evolutionary Model ◽  
Two Dimensional ◽  
Random Genetic Drift ◽  
Language Programs ◽  
Significant Events ◽  
History Of

We introduce a method for visualizing evolutionary activity of genotypes. Following a proposal of Bedau and Packard [11], we define a genotype's evolutionary activity in terms of the history of its concentration in the evolving population. To visualize this evolutionary activity we graph the distribution of evolutionary activity in the population of genotypes as a function of time. Adaptively significant genotypes trace a salient line or “wave” in these graphs. The quality of these waves indicates a variety of evolutionary phenomena, such as competitive exclusion, neutral variation, and random genetic drift. We apply this method in an evolutionary model of self-replicating assembly language programs competing for room in a two-dimensional space. Comparison with fitness graphs and with a nonadaptive analogue of this model shows how this method highlights adaptively significant events.

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