Abstract
For a graph G = ( V , E ) , a subset D ⊆ V is an r-hop dominating set if every vertex u ∈ V − D is at most r-hops away from D. It is a 2-connected r-hop dominating set if the subgraph of G induced by D is 2-connected. In this paper, we present two approximation algorithms to compute minimum 2-connected r-hop dominating set. The first one is a greedy algorithm using ear decomposition of 2-connected graphs. This algorithm is applicable to any 2-connected general graph. The second one is a three-phase algorithm which is only applicable to unit disk graphs. For both algorithms, performance ratios are given.
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