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Feedback vertex set
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Feedback vertex set : ウィキペディア英語版
Feedback vertex set
In the mathematical discipline of graph theory, a feedback vertex set of a graph is a set of vertices whose removal leaves a graph without cycles. In other words, each feedback vertex set contains at least one vertex of any cycle in the graph.
The feedback vertex set problem is an NP-complete problem in computational complexity theory. It was among the first problems shown to be NP-complete. It has wide applications in operating systems, database systems, and VLSI chip design.
== Definition ==

The decision problem is as follows:
:INSTANCE: An (undirected or directed) graph G = (V, E) and a positive integer k.
:QUESTION: Is there a subset X \subseteq V with |X| \leq k such that G with the vertices from X deleted is cycle-free?
The graph G(\setminus X ) that remains after removing X from G is an induced forest (resp. an induced directed acyclic graph in the case of directed graphs). Thus, finding a minimum feedback vertex set in a graph is equivalent to finding a maximum induced forest (resp. maximum induced directed acyclic graph in the case of directed graphs).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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