A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum-connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum-connected dominating set in unit-disk graphs. In this paper, we design a (1 ؉ 1/s)-approximation for the minimum-connected dominating set in unit-disk graphs, running in time n O ((s log s) 2 ).
Solid-state lithium batteries (SSBs) promise high energy and power densities, as well as enhanced safety, owing to the use of Li metal and nonflammable solid-state electrolytes.
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