1 research outputs found
Algorithm and Hardness results on Liar's Dominating Set and -tuple Dominating Set
Given a graph , the dominating set problem asks for a minimum subset
of vertices such that every vertex is
adjacent to at least one vertex . That is, the set satisfies the
condition that for each , where is the
closed neighborhood of . In this paper, we study two variants of the
classical dominating set problem: \boldmath{k}-tuple dominating set (-DS)
problem and Liar's dominating set (LDS) problem, and obtain several algorithmic
and hardness results.
On the algorithmic side, we present a constant factor
()-approximation algorithm for the Liar's dominating set problem
on unit disk graphs. Then, we obtain a PTAS for the \boldmath{k}-tuple
dominating set problem on unit disk graphs. On the hardness side, we show a
bits lower bound for the space complexity of any (randomized)
streaming algorithm for Liar's dominating set problem as well as for the
\boldmath{k}-tuple dominating set problem. Furthermore, we prove that the
Liar's dominating set problem on bipartite graphs is W[2]-hard.Comment: Appears in the Proceedings of the 30th International Workshop on
Combinatorial Algorithms (IWOCA 2019