Geodesic
A Distributed Algorithm for Minimum Distance-k Domination in Trees
Journal of Graph Algorithms and Applications, Tome 19 (2015) no. 1, pp. 223-242.

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While efficient algorithms for finding minimal distance-k dominating sets exist, finding minimum such sets is NP-hard even for bipartite graphs. This paper presents a distributed algorithm to determine a minimum (connected) distance-k dominating set and a maximum distance-2k independent set of a tree T. It terminates in O(height(T)) rounds and uses O(logk) space. To the best of our knowledge this is the first distributed algorithm that computes a minimum (as opposed to a minimal) distance-k dominating set for trees. The algorithm can also be applied to general graphs, albeit the distance-k dominating sets are not necessarily minimal. 
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     author = {Volker Turau and Sven K\"ohler},
     title = {A {Distributed} {Algorithm} for {Minimum} {Distance-k} {Domination} in {Trees}},
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Volker Turau; Sven Köhler. A Distributed Algorithm for Minimum Distance-k Domination in Trees. Journal of Graph Algorithms and Applications, Tome 19 (2015) no. 1, pp. 223-242. doi : 10.7155/jgaa.00354. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00354/

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