The Generalized Independent and Dominating Set Problems on Unit Disk Graphs
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In this article, we study a generalized version of the maximum independent set and minimum dominating set problems, namely, the maximum d-distance independent set problem and the minimum d-distance dominating set problem on unit disk graphs for a positive integer d>0. We first show that the maximum d-distance independent set problem and the minimum d-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.
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