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找最大独立集问题-FindingaMaximalIndependentSet

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发布: 2016-06-07 15:57:09
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1. 独立集和最大独立集:A set of vertices I ? V is called independent if no pair of vertices in I is connected via an edge in G. An independent set is called maximal if by including any other vertex not in I, the independence property is vi

1. 独立集和最大独立集:A set of vertices I ? V is called independent if no pair of vertices in I is connected via an edge in G. An independent set is called maximal if by including any other vertex not in I, the independence property is violated.

下图是独立集和最大独立集的例子:

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2. Finding a Maximal Independent Set (MIS)

1) Simple algorithms start byMIS I to be empty, and assigning all vertices to a candidate set C. Each vertex generates a(unique) random number and communicates it to its neighbZ喎?http://www.2cto.com/kf/ware/vc/" target="_blank" class="keylink">vcnMuPGJyPgoyKSBJZiB2ZXJ0ZXggdg=="s number less than that of all its neighbors, it joins set I. All of its neighbors are removed from C.
3) This process continuesuntil C is empty.

On average, this algorithmconverges after O(log|V|) such steps. 下图是找MIS的例子:

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