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تسجيل مستخدم جديدTotal Domination in Unit Disk Graphs
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نشر من قبل
Sangram Kishor Jena Mr
تاريخ النشر
2020
مجال البحث
الهندسة المعلوماتية
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English
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Let $G=(V,E)$ be an undirected graph. We call $D_t subseteq V$ as a total dominating set (TDS) of $G$ if each vertex $v in V$ has a dominator in $D$ other than itself. Here we consider the TDS problem in unit disk graphs, where the objective is to find a minimum cardinality total dominating set for an input graph. We prove that the TDS problem is NP-hard in unit disk graphs. Next, we propose an 8-factor approximation algorithm for the problem. The running time of the proposed approximation algorithm is $O(n log k)$, where $n$ is the number of vertices of the input graph and $k$ is output size. We also show that TDS problem admits a PTAS in unit disk graphs.
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