Abstract
In this paper we consider the classical connected dominating set problem. Twenty years ago, Guha and Khuller developed two algorithms for this problem—a centralized greedy approach with an approximation guarantee of \(H(\varDelta ) +2\), and a local information greedy approach with an approximation guarantee of \(2(H(\varDelta )+1)\) (where H() is the harmonic function, and \(\varDelta \) is the maximum degree in the graph). A local information greedy algorithm uses significantly less knowledge about the graph, and can be useful in a variety of contexts. However, a fundamental question remained—can we get a local information greedy algorithm with the same performance guarantee as the global greedy algorithm without the penalty of the multiplicative factor of “2” in the approximation factor? In this paper, we answer that question in the affirmative.
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This work was recently awarded the ESA Test of Time Award.
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This work is supported by NSF Grant CCF 1217890 and CCF 1655073 (Eager). A preliminary version of this work was published in APPROX-RANDOM 2016.
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Khuller, S., Yang, S. Revisiting Connected Dominating Sets: An Almost Optimal Local Information Algorithm. Algorithmica 81, 2592–2605 (2019). https://doi.org/10.1007/s00453-019-00545-0
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DOI: https://doi.org/10.1007/s00453-019-00545-0