On container length and wide-diameter in unidirectional hypercubes

Lu Changhong; Zhang Kemin

doi:10.11650/twjm/1500407401

On container length and wide-diameter in unidirectional hypercubes

Lu Changhong, Zhang Kemin

Nanjing University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, two unidirectional binary n-cubes, namely, Q₁ (n) and Q₂H, proposed as high-speed networking schemes by Chou and Du, are studied. We show that the smallest possible length for any maximum fault-tolerant container from a to b is at most n + 2 whether a and b are in Q₁ (n) or in Q₂(n). Furthermore, we prove that the wide-diameters of Q₁(n) and Q₂(n) are equal to n + 2. At last, we show that a conjecture proposed by Jwo and Tuan is true.

Original language	English
Pages (from-to)	75-87
Number of pages	13
Journal	Taiwanese Journal of Mathematics
Volume	6
Issue number	1
DOIs	https://doi.org/10.11650/twjm/1500407401
State	Published - Mar 2002
Externally published	Yes

Keywords

Connectivity
Container
Hypercube
Wide-diameter

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10.11650/twjm/1500407401

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abstract = "In this paper, two unidirectional binary n-cubes, namely, Q1 (n) and Q2H, proposed as high-speed networking schemes by Chou and Du, are studied. We show that the smallest possible length for any maximum fault-tolerant container from a to b is at most n + 2 whether a and b are in Q1 (n) or in Q2(n). Furthermore, we prove that the wide-diameters of Q1(n) and Q2(n) are equal to n + 2. At last, we show that a conjecture proposed by Jwo and Tuan is true.",

keywords = "Connectivity, Container, Hypercube, Wide-diameter",

author = "Lu Changhong and Zhang Kemin",

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AU - Changhong, Lu

AU - Kemin, Zhang

PY - 2002/3

Y1 - 2002/3

N2 - In this paper, two unidirectional binary n-cubes, namely, Q1 (n) and Q2H, proposed as high-speed networking schemes by Chou and Du, are studied. We show that the smallest possible length for any maximum fault-tolerant container from a to b is at most n + 2 whether a and b are in Q1 (n) or in Q2(n). Furthermore, we prove that the wide-diameters of Q1(n) and Q2(n) are equal to n + 2. At last, we show that a conjecture proposed by Jwo and Tuan is true.

AB - In this paper, two unidirectional binary n-cubes, namely, Q1 (n) and Q2H, proposed as high-speed networking schemes by Chou and Du, are studied. We show that the smallest possible length for any maximum fault-tolerant container from a to b is at most n + 2 whether a and b are in Q1 (n) or in Q2(n). Furthermore, we prove that the wide-diameters of Q1(n) and Q2(n) are equal to n + 2. At last, we show that a conjecture proposed by Jwo and Tuan is true.

KW - Connectivity

KW - Container

KW - Hypercube

KW - Wide-diameter

UR - https://www.scopus.com/pages/publications/0040668387

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DO - 10.11650/twjm/1500407401

M3 - 文章

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SP - 75

EP - 87

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

IS - 1

ER -

On container length and wide-diameter in unidirectional hypercubes

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Keywords

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