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• W3038202234 abstract "We usually use a digraph to represent a wireless network (WN). Correspondingly, a connected dominating set (CDS) of the digraph is usually used to denote a virtual backbone (VB) of the corresponding WN. In this article, focusing on the problem of a minimum strongly connected dominating and absorbing set (MSCDAS) with a bounded diameter (or guaranteed routing cost) for a digraph, which is strongly connected, we introduce two algorithms. One is called the guaranteed routing cost strongly connected dominating and absorbing set (GOC-SCDAS), which can generate a strongly connected dominating and absorbing set (SCDAS) with a performance ratio <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mn>14.4</mml:mn><mml:msup><mml:mrow><mml:mfenced open=( close=)><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mfenced open=( close=)><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> in respect of the optimal solution. Another is called the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>α</mml:mi></mml:math> guaranteed routing cost strongly connected bidirectional dominating and absorbing set (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>α</mml:mi></mml:math>-GOC-SCBDAS), which can generate a strongly connected bidirectional dominating and absorbing set (SCBDAS) with a performance ratio <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mn>8.844</mml:mn><mml:msup><mml:mrow><mml:mfenced open=( close=)><mml:mrow><mml:mn>3</mml:mn><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mfenced open=( close=)><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mfenced open=( close=)><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mfenced open=( close=)><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> in respect of the optimal solution and a better routing cost, where <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>max</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>min</mml:mi></mml:mrow></mml:msub></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mfenced open=[ close=]><mml:mrow><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>min</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>max</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:math> is the transmission range of nodes in the network. Through the simulation experiments, we obtain the conclusion that in terms of the diameter and average routing path length (ARPL) of CDS, the outputs of our algorithms are better than those of the algorithm in (Du et al. 2006)." @default.
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• W3038202234 date "2020-07-04" @default.
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• W3038202234 title "The Construction of a Virtual Backbone with a Bounded Diameter in a Wireless Network" @default.
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