On average edge length of minimum spanning trees

Given a set S of points in the plane, a geometric network for S is a graph G with vertex set S and straight edges. We consider a broadcasting situation, where one point r ∊ S is a designated source. Given a dilation factor δ, we ask for a geometric network G such that for every point v ∊ S there is a path from r to v in G of length at most δ|rv|, and such that the total edge length is minimized. We show that finding such a network of minimum total edge length is NP-hard, and give an approximation algorithm.

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Parallel Update of Minimum Spanning Trees in Logarithmic Time.

10.21236/ada150497 ◽

1984 ◽

Cited By ~ 1

Author(s):

I. V. Ramakrishnan ◽

S. Pawagi

Keyword(s):

Spanning Trees ◽

Minimum Spanning Trees

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Identification of Dementia Related Brain Functional Networks with Minimum Spanning Trees

2020 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) ◽

10.1109/bibm49941.2020.9313223 ◽

2020 ◽

Author(s):

Abdulyekeen. T. Adebisi ◽

Venkateswarlu Gonuguntla ◽

Ho-Won Lee ◽

Kalyana. C. Veluvolu

Keyword(s):

Spanning Trees ◽

Functional Networks ◽

Minimum Spanning Trees ◽

Brain Functional Networks

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A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning Trees

ACM Transactions on Algorithms ◽

10.1145/3365005 ◽

2020 ◽

Vol 16 (1) ◽

pp. 1-27

Author(s):

Gopal Pandurangan ◽

Peter Robinson ◽

Michele Scquizzato

Keyword(s):

Distributed Algorithm ◽

Spanning Trees ◽

Minimum Spanning Trees

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Facile Synthesis of Cu2O Nanocubes in Triblock Copolymer Solutions

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.121-123.275 ◽

2007 ◽

Vol 121-123 ◽

pp. 275-278

Author(s):

Jin Hua Jiang ◽

Qiu Ming Gao

Keyword(s):

Triblock Copolymer ◽

Solar Spectrum ◽

Blue Shift ◽

Edge Length ◽

Promising Candidate ◽

Organic Species ◽

Transmission Electron ◽

Ft Ir ◽

Average Edge Length

Cuprous oxide and related materials in nanosizes are of much interest and investigated extensively recently. It is reported here that cubic Cu2O nanocubes were synthesized successfully in aqueous solutions at room temperature in air condition. Copper (II) salts in water were reduced with ascorbate acid in air, using the nonionic pluronic amphiphilic triblock copolymer EO20PO70EO20 (P123) as the template-directing and protecting agent. The average edge length of the cubes varied from 50 to 100 nm. Transmission electron microscopy (TEM) has been used for the shape and structural characterization of the obtained Cu2O nanocubes. The UV-Vis spectra showed an obvious blue-shift (0.53 eV), compared to the band gap of the bulk Cu2O crystal, which makes it a promising candidate in solar energy conversion since this sample can make use of higher energy visible rays of solar spectrum. In the FT-IR spectra the peak of Cu-O bond for the Cu2O is clearly distinguished and several weak peaks of the C-H, C-C and C=O bonds for the organic species can also be detectable, implying a little P123 residua in the products. The effect of the triblock copolymer P123 on the growth of the Cu2O nanocubes is discussed.

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