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A feedback vertex set (FVS) of an undirected graph is a set of vertices that contains at least one vertex of each cycle of the graph.The feedback vertex set problem consists of constructing a FVS of size less than certain given value.This combinatorial optimization problem has many practical applications,but it can be extremely difficult to solve as it belongs to the nondeterministic polynomial-complete (NP-complete) class of worst-case computational complexity.