article

Distributed minimum dominating set approximations in restricted families of graphs

Authors:

Christoph Lenzen,

Yvonne-Anne Pignolet,

Roger WattenhoferAuthors Info & Claims

Distributed Computing, Volume 26, Issue 2

Pages 119 - 137

https://doi.org/10.1007/s00446-013-0186-z

Published: 01 April 2013 Publication History

Abstract

A dominating set is a subset of the nodes of a graph such that all nodes are in the set or adjacent to a node in the set. A minimum dominating set approximation is a dominating set that is not much larger than a dominating set with the fewest possible number of nodes. This article summarizes the state-of-the-art with respect to finding minimum dominating set approximations in distributed systems, where each node locally executes a protocol on its own, communicating with its neighbors in order to achieve a solution with good global properties. Moreover, we present a number of recent results for specific families of graphs in detail. A unit disk graph is given by an embedding of the nodes in the Euclidean plane, where two nodes are joined by an edge exactly if they are in distance at most one. For this family of graphs, we prove an asymptotically tight lower bound on the trade-off between time complexity and approximation ratio of deterministic algorithms. Next, we consider graphs of small arboricity, whose edge sets can be decomposed into a small number of forests. We give two algorithms, a randomized one excelling in its approximation ratio and a uniform deterministic one which is faster and simpler. Finally, we show that in planar graphs, which can be drawn in the Euclidean plane without intersecting edges, a constant approximation factor can be ensured within a constant number of communication rounds.

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Heydt OKublenz SOssona de Mendez PSiebertz SVigny A(2025)Distributed domination on sparse graph classesEuropean Journal of Combinatorics10.1016/j.ejc.2023.103773123:COnline publication date: 1-Jan-2025
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Distributed minimum dominating set approximations in restricted families of graphs
1. Mathematics of computing
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cover image Distributed Computing

Distributed Computing Volume 26, Issue 2

April 2013

61 pages

ISSN:0178-2770

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Copyright © Copyright © 2013 Springer-Verlag Berlin Heidelberg.

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 April 2013

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https://dl.acm.org/doi/10.1016/j.ejc.2023.103773
Chang Y(2024)The energy complexity of diameter and minimum cut computation in bounded-genus networksTheoretical Computer Science10.1016/j.tcs.2023.114279982:COnline publication date: 8-Jan-2024
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Dory MGhaffari MIlchi S(2024)Near-optimal distributed dominating set in bounded arboricity graphsDistributed Computing10.1007/s00446-023-00447-z37:4(387-398)Online publication date: 1-Dec-2024
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