A greedy algorithm for the fault-tolerant outer-connected dominating set problem

Xiaozhi Wang, Xianyue Li, Bo Hou, Wen Liu, Lidong Wu () and Suogang Gao ()
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Xiaozhi Wang: Hebei Normal University
Xianyue Li: Lanzhou University
Bo Hou: Hebei Normal University
Wen Liu: Hebei Normal University
Lidong Wu: University of Texas at Tyler
Suogang Gao: Hebei Normal University

Journal of Combinatorial Optimization, 2021, vol. 41, issue 1, No 9, 118-127

Abstract: Abstract For a graph $$G=(V,E)$$ G = ( V , E ) , a vertex set $$C\subseteq V$$ C ⊆ V is an m-fold outer-connected dominating set (m-fold OCDS) of G if every vertex in $$V\backslash C$$ V \ C has at least m neighbors in C and the subgraph of G induced by $$V\backslash C$$ V \ C is connected. In this paper, we present a greedy algorithm to compute an m-fold OCDS in general graphs, which returns a solution of size at most $$\alpha +1+\ln (\Delta +m+1)$$ α + 1 + ln ( Δ + m + 1 ) times that of a minimum m-fold OCDS, where $$\Delta $$ Δ is the maximum degree of the graph and $$\alpha $$ α is a positive number at most $$\Delta $$ Δ +m+1.

Keywords: m-Fold outer-connected dominating set; Potential function; Greedy algorithm; Submodular (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10878-020-00668-z

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