A linear time algorithm for optimal k-hop dominating set of a tree

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• 作者：Sukhamay Kundu^a ; ^{kundu@csc.lsu.edu" class="auth_mail" title="E-mail the corresponding author} ; Subhashis Majumder^b ; ^{subhashis.majumder@heritageit.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Graph algorithms ; k-Hop dominating set ; Rooted tree
• 刊名：Information Processing Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：116
• 期：2
• 页码：197-202
• 全文大小：362 K

文摘

We give a linear time algorithm to compute an optimal (minimum) k-hop dominating set D of a tree T   for k≥1$k\ge 1$. This extends the previous result for an optimal 1-dominating set for trees. We use a rooted form $\overline{T}$ of T, with an arbitrary node selected as the root, to direct the search for nodes of D in a bottom–up fashion. The decision whether to include a node x in D   or not is based on the subtree of $\overline{T}$ at x. Optimal k-hop dominating sets have many important practical applications.