简短声明:超快的t-ruling sets

Tushar Bisht, Kishore Kothapalli, S. Pemmaraju
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引用次数: 20

摘要

图G = (V, E)的t-统治集是一个独立的、满足每个顶点V∈V与S中的某个顶点相距不超过t跳的性质的顶点子集S。最大独立集(MIS)是一个1统治集。本文扩展了Kothapalli et al. (FSTTCS 2012)的结果,提出了一种随机算法,用于高概率地计算t-统治集,对于2 < t≤√(log log n),在O(t·log1/(t-1)n)轮中,对于t >√(log log n),在(O(√(log log n)))轮中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Brief announcement: Super-fast t-ruling sets
A t-ruling set of a graph G = (V, E) is a vertex-subset S ⊆ V that is independent and satisfies the property that every vertex v ∈ V is at a distance of at most t hops from some vertex in S. A maximal independent set (MIS) is a 1-ruling set. Extending results from Kothapalli et al. (FSTTCS 2012) this note presents a randomized algorithm for computing, with high probability, a t-ruling set in O(t ⋅ log1/(t-1)n) rounds for 2 < t ≤ √(log log n) and in (O(√(log log n))) rounds for t > √(log log n).
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