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A Linear Time Self-stabilizing Algorithm for Minimal Weakly Connected Dominating Sets

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Abstract

In this paper, we propose a new self-stabilizing algorithm for minimal weakly connected dominating sets (called algorithm \(\mathtt{MWCDS}\)). For an arbitrary connected graph with \(n\) nodes, algorithm \(\mathtt{MWCDS}\) terminates in \(O(n)\) steps using a synchronous daemon. The space requirement at each node is \(O(\log n)\) bits. In the literature, the best reported stabilization time for a minimal weakly connected dominating set algorithm is \(O(nmA)\) under a distributed daemon, where \(m\) is the number of edges and \(A\) is the number of moves to construct a breadth-first tree.

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Authors and Affiliations

  1. School of Computing, Clemson University, Clemson, SC, 29634, USA

    Yihua Ding, James Z. Wang & Pradip K. Srimani

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  1. Yihua Ding
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  2. James Z. Wang
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  3. Pradip K. Srimani
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Correspondence to Pradip K. Srimani.

Additional information

This research was partly supported by National Science Foundation (DBI-0960586 and DBI-0960443); Guangzhou Science and Technology Fund of China (2012J4300038, LCY201206, and 2013J4300061); and Guangdong Science and Technology Fund of China (2012B091100221).

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Ding, Y., Wang, J.Z. & Srimani, P.K. A Linear Time Self-stabilizing Algorithm for Minimal Weakly Connected Dominating Sets. Int J Parallel Prog 44, 151–162 (2016). https://doi.org/10.1007/s10766-014-0335-4

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  • DOI: https://doi.org/10.1007/s10766-014-0335-4

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