Abstract
The existence and efficient finding of small dominating sets in dense random graphs is examined in this work. We show, for the model G n,p with p=1/2, that:
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1.
The probability of existence of dominating sets of size less than log n tends to zero as n tends to infinity.
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2.
Dominating sets of size [log n] exist almost surely.
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3.
We provide two algorithms which construct small dominating sets in G n, 1/2 run in O (n alog n) time (on the average and also with high probability). Our algorithms almost surely construct a dominating set of size at most (1+ε) log n, for any fixed ε > 0.
Our results extend to the case Gn,p with p fixed to any constant < 1.
This research is partially supported by the ESPRIT Basic Research Action Nr 7141 (ALCOM II) and by the Ministry of Education of Greece.
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© 1994 Springer-Verlag Berlin Heidelberg
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Nikoletseas, S.E., Spirakis, P.G. (1994). Near-optimal dominating sets in dense random graphs in polynomial expected time. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_36
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DOI: https://doi.org/10.1007/3-540-57899-4_36
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