scholarly journals A tight upper bound for the path length of AVL trees

1990 ◽  
Vol 72 (2-3) ◽  
pp. 251-264 ◽  
Author(s):  
Rolf Klein ◽  
Derick Wood
Keyword(s):  
Upper Bound ◽  
Path Length ◽  
Avl Trees

scholarly journals MULTIDIMENSIONAL ONLINE MOTION PLANNING FOR A SPHERICAL ROBOT

2010 ◽  
Vol 20 (06) ◽  
pp. 653-684 ◽  
Author(s):  
JOSH BROWN KRAMER ◽  
LUCAS SABALKA
Keyword(s):  
Motion Planning ◽  
Upper Bound ◽  
Path Length ◽  
Online Algorithm ◽  
Optimal Path ◽  
Spherical Robot ◽  
Global Positioning ◽  
Non Linear ◽  
Arbitrary Dimensions ◽  
Competitive Algorithms

We consider three related problems of robot movement in arbitrary dimensions: coverage, search, and navigation. For each problem, a spherical robot is asked to accomplish a motion-related task in an unknown environment whose geometry is learned by the robot during navigation. The robot is assumed to have tactile and global positioning sensors. We view these problems from the perspective of (non-linear) competitiveness as defined by Gabriely and Rimon. We first show that in 3 dimensions and higher, there is no upper bound on competitiveness: every online algorithm can do arbitrarily badly compared to the optimal. We then modify the problems by assuming a fixed clearance parameter. We are able to give optimally competitive algorithms under this assumption. We show that these modified problems have polynomial competitiveness in the optimal path length, of degree equal to the dimension.

scholarly journals A NEW WEIGHT BALANCED BINARY SEARCH TREE

2000 ◽  
Vol 11 (03) ◽  
pp. 485-513 ◽  
Author(s):  
SEONGHUN CHO ◽  
SARTAJ SAHNI
Keyword(s):  
Path Length ◽  
Search Time ◽  
Search Tree ◽  
Binary Search ◽  
Experimental Results ◽  
Binary Search Tree ◽  
Binary Search Trees ◽  
Search Trees ◽  
New Class ◽  
Avl Trees

We develop a new class of weight balanced binary search trees called β-balanced binary search trees (β-BBSTs). β-BBSTs are designed to have reduced internal path length. As a result, they are expected to exhibit good search time characteristics. Individual search, insert, and delete operations in an n node β-BBST take O( log n) time for [Formula: see text]. Experimental results comparing the performance of β-BBSTs, WB(α) trees, AVL-trees, red/black trees, treaps, deterministic skip lists and skip lists are presented. Two simplified versions of, β-BBSTs are also developed.

The Effect of Path Length and Display Size on Memory for Spatial Information

2012 ◽  
Vol 59 (3) ◽  
pp. 147-152 ◽  
Author(s):  
Katherine Guérard ◽  
Sébastien Tremblay
Keyword(s):  
Path Length ◽  
Potential Role ◽  
Spatial Information ◽  
Recall Performance ◽  
Minor Role ◽  
Length Effect ◽  
Serial Memory ◽  
Fixed Reference ◽  
A Minor

In serial memory for spatial information, some studies showed that recall performance suffers when the distance between successive locations increases relatively to the size of the display in which they are presented (the path length effect; e.g., Parmentier et al., 2005) but not when distance is increased by enlarging the size of the display (e.g., Smyth & Scholey, 1994). In the present study, we examined the effect of varying the absolute and relative distance between to-be-remembered items on memory for spatial information. We manipulated path length using small (15″) and large (64″) screens within the same design. In two experiments, we showed that distance was disruptive mainly when it is varied relatively to a fixed reference frame, though increasing the size of the display also had a small deleterious effect on recall. The insertion of a retention interval did not influence these effects, suggesting that rehearsal plays a minor role in mediating the effects of distance on serial spatial memory. We discuss the potential role of perceptual organization in light of the pattern of results.

Investigation of particulate systems using optical pathlength spectroscopy

2000 ◽  
Vol 627 ◽  
Author(s):  
Gabriel Popescu ◽  
Aristide Dogariu
Keyword(s):  
Path Length ◽  
Random Media ◽  
Michelson Interferometer ◽  
Industrial Process ◽  
Optical Path Length ◽  
Industrial Applications ◽  
Optical Path ◽  
Interference Signal ◽  
Optical Length ◽  
Reference Mirror

ABSTRACTIn many industrial applications involving granular media, knowledge about the structural transformations suffered during the industrial process is desirable. Optical techniques are noninvasive, fast, and versatile tools for monitoring such transformations. We have recently introduced optical path-length spectroscopy as a new technique for random media investigation. The principle of the method is to use a partially coherent source in a Michelson interferometer, where the fields from a reference mirror and the sample are combined to obtain an interference signal. When the system under investigation is a multiple-scattering medium, by tuning the optical length of the reference arm, the optical path-length probability density of light backscattered from the sample is obtained. This distribution carries information about the structural details of the medium. In the present paper, we apply the technique of optical path-length spectroscopy to investigate inhomogeneous distributions of particulate dielectrics such as ceramics and powders. The experiments are performed on suspensions of systems with different solid loads, as well as on powders and suspensions of particles with different sizes. We show that the methodology is highly sensitive to changes in volume concentration and particle size and, therefore, it can be successfully used for real-time monitoring. In addition, the technique is fiber optic-based and has all the advantages associated with the inherent versatility.

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