Abstract
Suppose that in a network, a node can dominate (or cover, monitor, etc) its neighbor nodes. An interesting question asks to find such a minimum set of nodes that dominate all the other nodes. This is known as the minimum dominating set problem. A natural generalization assumes that a node can dominate nodes within a distance R ≥ 1, called the minimum distance dominating set problem. On the other hand, if the distance between any two nodes in the dominating set must be at least z ≥ 1, then the problem is known as the minimum independent dominating set problem. This paper considers to find a minimum distance-R independence-z dominating set for arbitrary R and z, which has applications in facility location, internet monitoring and others. We show a practical approach. Empirical studies show that usually it is very fast and quite accurate, thus suitable for Big Data analysis. Generalization to directed graphs, edge lengths, multi-dominating are also discussed.
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Zhao, L., Kadowaki, H., Wagner, D. (2013). A Practical Approach for Finding Small {Independent, Distance} Dominating Sets in Large-Scale Graphs. In: Aversa, R., Kołodziej, J., Zhang, J., Amato, F., Fortino, G. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2013. Lecture Notes in Computer Science, vol 8286. Springer, Cham. https://doi.org/10.1007/978-3-319-03889-6_18
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DOI: https://doi.org/10.1007/978-3-319-03889-6_18
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03888-9
Online ISBN: 978-3-319-03889-6
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