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The Generalized Independent and Dominating Set Problems on Unit Disk Graphs
In this article, we study a generalized version of the maximum independent
set and minimum dominating set problems, namely, the maximum -distance
independent set problem and the minimum -distance dominating set problem on
unit disk graphs for a positive integer . We first show that the maximum
-distance independent set problem and the minimum -distance dominating
set problem belongs to NP-hard class. Next, we propose a simple polynomial-time
constant-factor approximation algorithms and PTAS for both the problems