scholarly journals A Binomial Splitting Process in Connection with Corner Parking Problems

2014 ◽  
Vol 51 (04) ◽  
pp. 971-989 ◽  
Author(s):  
Michael Fuchs ◽  
Hsien-Kuei Hwang ◽  
Yoshiaki Itoh ◽  
Hosam H. Mahmoud
Keyword(s):  
Data Structures ◽  
High Dimensional ◽  
Logarithmic Mean ◽  
Occupancy Problem ◽  
Tree Data ◽  
Bounded Variance ◽  
Binomial Parameter ◽  
Practical Algorithm ◽  
Periodic Fluctuations ◽  
Splitting Process

This paper studies a special type of binomial splitting process. Such a process can be used to model a high dimensional corner parking problem as well as determining the depth of random PATRICIA (practical algorithm to retrieve information coded in alphanumeric) tries, which are a special class of digital tree data structures. The latter also has natural interpretations in terms of distinct values in independent and identically distributed geometric random variables and the occupancy problem in urn models. The corresponding distribution is marked by a logarithmic mean and a bounded variance, which is oscillating, if the binomial parameter p is not equal to ½, and asymptotic to one in the unbiased case. Also, the limiting distribution does not exist as a result of the periodic fluctuations.

scholarly journals A Binomial Splitting Process in Connection with Corner Parking Problems

2014 ◽  
Vol 51 (4) ◽  
pp. 971-989 ◽  
Author(s):  
Michael Fuchs ◽  
Hsien-Kuei Hwang ◽  
Yoshiaki Itoh ◽  
Hosam H. Mahmoud
Keyword(s):  
Data Structures ◽  
High Dimensional ◽  
Logarithmic Mean ◽  
Occupancy Problem ◽  
Tree Data ◽  
Bounded Variance ◽  
Binomial Parameter ◽  
Practical Algorithm ◽  
Periodic Fluctuations ◽  
Splitting Process

This paper studies a special type of binomial splitting process. Such a process can be used to model a high dimensional corner parking problem as well as determining the depth of random PATRICIA (practical algorithm to retrieve information coded in alphanumeric) tries, which are a special class of digital tree data structures. The latter also has natural interpretations in terms of distinct values in independent and identically distributed geometric random variables and the occupancy problem in urn models. The corresponding distribution is marked by a logarithmic mean and a bounded variance, which is oscillating, if the binomial parameterpis not equal to ½, and asymptotic to one in the unbiased case. Also, the limiting distribution does not exist as a result of the periodic fluctuations.

Recursive proofs for inductive tree data-structures

2012 ◽  
Vol 47 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Parthasarathy Madhusudan ◽  
Xiaokang Qiu ◽  
Andrei Stefanescu
Keyword(s):  
Data Structures ◽  
Tree Data

scholarly journals Depicting More Information in Enriched Squarified Treemaps with Layered Glyphs

Information ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 123
Author(s):  
Anderson Gregório Marques Soares ◽  
Elvis Thermo Carvalho Miranda ◽  
Rodrigo Santos do Amor Divino Lima ◽  
Carlos Gustavo Resque dos Santos ◽  
Bianchi Serique Meiguins
Keyword(s):  
Information Visualization ◽  
Data Structures ◽  
User Study ◽  
Relevant Information ◽  
Data Representation ◽  
High Dimensional ◽  
Hierarchical Data ◽  
Visual Data ◽  
Visual Variable ◽  
Data Clusters

The Treemap is one of the most relevant information visualization (InfoVis) techniques to support the analysis of large hierarchical data structures or data clusters. Despite that, Treemap still presents some challenges for data representation, such as the few options for visual data mappings and the inability to represent zero and negative values. Additionally, visualizing high dimensional data requires many hierarchies, which can impair data visualization. Thus, this paper proposes to add layered glyphs to Treemap’s items to mitigate these issues. Layered glyphs are composed of N partially visible layers, and each layer maps one data dimension to a visual variable. Since the area of the upper layers is always smaller than the bottom ones, the layers can be stacked to compose a multidimensional glyph. To validate this proposal, we conducted a user study to compare three scenarios of visual data mappings for Treemaps: only Glyphs (G), Glyphs and Hierarchy (GH), and only Hierarchy (H). Thirty-six volunteers with a background in InfoVis techniques, organized into three groups of twelve (one group per scenario), performed 8 InfoVis tasks using only one of the proposed scenarios. The results point that scenario GH presented the best accuracy while having a task-solving time similar to scenario H, which suggests that representing more data in Treemaps with layered glyphs enriched the Treemap visualization capabilities without impairing the data readability.

Multiresolution image registration based on tree data structures

2011 ◽  
Vol 73 (4) ◽  
pp. 111-126 ◽  
Author(s):  
Anton Bardera ◽  
Imma Boada ◽  
Miquel Feixas ◽  
Jaume Rigau ◽  
Mateu Sbert
Keyword(s):  
Image Registration ◽  
Data Structures ◽  
Tree Data ◽  
Multiresolution Image

Teaching of tree data structures using microcomputer graphics

1986 ◽  
Vol 18 (1) ◽  
pp. 67-72 ◽  
Author(s):  
G. Scott Owen
Keyword(s):  
Data Structures ◽  
Tree Data

scholarly journals MERGEABLE DOUBLE-ENDED PRIORITY QUEUES

1999 ◽  
Vol 10 (01) ◽  
pp. 1-17 ◽  
Author(s):  
SEONGHUN CHO ◽  
SARTAJ SAHNI
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
Priority Queue ◽  
Priority Queues ◽  
Experimental Results ◽  
Tree Data ◽  
Tree Data Structure

We show that the leftist tree data structure may be adapted to obtain data structures that permit the double-ended priority queue operations Insert, DeleteMin, DeleteMax, and Merge to be done in O( log n) time where n is the size of the resulting queue. The operations FindMin and FindMax can be done in O(1) time. Experimental results are also presented.

On Structural Signatures for Tree Data Structures

2012 ◽  
pp. 171-187 ◽  
Author(s):  
Kai Samelin ◽  
Henrich C. Pöhls ◽  
Arne Bilzhause ◽  
Joachim Posegga ◽  
Hermann de Meer
Keyword(s):  
Data Structures ◽  
Tree Data
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