# Square-root rule of two-dimensional bandwidth problem

• Volume: 45, Issue: 4, page 399-411
• ISSN: 0988-3754

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## Abstract

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The bandwidth minimization problem is of significance in network communication and related areas. Let G be a graph of n vertices. The two-dimensional bandwidth B2(G) of G is the minimum value of the maximum distance between adjacent vertices when G is embedded into an n × n grid in the plane. As a discrete optimization problem, determining B2(G) is NP-hard in general. However, exact results for this parameter can be derived for some special classes of graphs. This paper studies the “square-root rule” of the two-dimensional bandwidth, which is useful in evaluating B2(G) for some typical graphs.

## How to cite

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Lin, Lan, and Lin, Yixun. "Square-root rule of two-dimensional bandwidth problem." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 45.4 (2011): 399-411. <http://eudml.org/doc/273000>.

@article{Lin2011,
abstract = {The bandwidth minimization problem is of significance in network communication and related areas. Let G be a graph of n vertices. The two-dimensional bandwidth B2(G) of G is the minimum value of the maximum distance between adjacent vertices when G is embedded into an n × n grid in the plane. As a discrete optimization problem, determining B2(G) is NP-hard in general. However, exact results for this parameter can be derived for some special classes of graphs. This paper studies the “square-root rule” of the two-dimensional bandwidth, which is useful in evaluating B2(G) for some typical graphs.},
author = {Lin, Lan, Lin, Yixun},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {network layout; two-dimensional bandwidth; lower and upper bounds; optimal embedding; network communication; square root rule; bandwidth minimization problem},
language = {eng},
number = {4},
pages = {399-411},
publisher = {EDP-Sciences},
title = {Square-root rule of two-dimensional bandwidth problem},
url = {http://eudml.org/doc/273000},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Lin, Lan
AU - Lin, Yixun
TI - Square-root rule of two-dimensional bandwidth problem
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 4
SP - 399
EP - 411
AB - The bandwidth minimization problem is of significance in network communication and related areas. Let G be a graph of n vertices. The two-dimensional bandwidth B2(G) of G is the minimum value of the maximum distance between adjacent vertices when G is embedded into an n × n grid in the plane. As a discrete optimization problem, determining B2(G) is NP-hard in general. However, exact results for this parameter can be derived for some special classes of graphs. This paper studies the “square-root rule” of the two-dimensional bandwidth, which is useful in evaluating B2(G) for some typical graphs.
LA - eng
KW - network layout; two-dimensional bandwidth; lower and upper bounds; optimal embedding; network communication; square root rule; bandwidth minimization problem
UR - http://eudml.org/doc/273000
ER -

## References

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9. [9] L. Lin and Y. Lin, Two models of two-dimensional bandwidth problems, Inform. Process. Lett.110 (2010) 469–473. Zbl1229.68058MR2667148
10. [10] J. Mai and H. Luo, Some theorems on the bandwidth of a graph. Acta Math. Appl. Sinica7 (1984) 86–95. Zbl0542.05052MR768053
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