A New Approximation Algorithm for Minimum-Weight (1,m)–Connected Dominating Set

01/23/2023

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by   Jiao Zhou, et al.

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Consider a graph with nonnegative node weight. A vertex subset is called a CDS (connected dominating set) if every other node has at least one neighbor in the subset and the subset induces a connected subgraph. Furthermore, if every other node has at least m neighbors in the subset, then the node subset is called a (1,m)CDS. The minimum-weight (1,m)CDS problem aims at finding a (1,m)CDS with minimum total node weight. In this paper, we present a new polynomial-time approximation algorithm for this problem with approximation ratio 2H(δ_max+m-1), where δ_max is the maximum degree of the given graph and H(·) is the Harmonic function, i.e., H(k)=∑_i=1^k 1/i.