Linear-Time Kernelization for Feedback Vertex Set

  title={Linear-Time Kernelization for Feedback Vertex Set},
  author={Yoichi Iwata},
In this paper, we propose an algorithm that, given an undirected graph G of m edges and an integer k, computes a graph G′ and an integer k′ in O(km) time such that (1) the size of the graph G′ is O(k), (2) k′ ≤ k, and (3) G has a feedback vertex set of size at most k if and only if G′ has a feedback vertex set of size at most k′. This is the first linear-time polynomial-size kernel for Feedback Vertex Set. The size of our kernel is 2k + k vertices and 4k edges, which is smaller than the… CONTINUE READING
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