feedback vertex set solver
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feedback vertex set solver

This is an exact solver for feedback vertex set problem that won 1st place in the 1st Parameterized Algorithms and Computational Experiments Challenge ( Preliminary results against the public data set: result.tsv

Implemented algorithms

  • Linear-time kernel ( (
    • This algorithm runs in O(k^4 m) time, where k is the solution size, and produces an equivalent instance of size at most 2k^2+k vertices and 4k^2 edges.
    • Using the following set of reductions:
      • the basic reductions (self-loop, degree at most 2)
      • s-cycle cover reduction by an efficient augmentaing-path algorithm for solving the k-submodular relaxation (
      • + several heuristic reductions (these reductions are correct but would not improve the theoretical worst-case perfomance)
  • FPT branch-and-bound ( (
    • This algorithm runs in O^*(4^k) time.
    • At each node of the search tree, we apply the following set of reductions (
      • the basic reductions
      • persistency reduction
      • + several heuristic reductions
    • Using the following lewer bounds to prune the search
      • k-submodular relaxation lower bound computed by the efficient augmenting-path algorithm
      • lower bound used for bounding the kernel size (


Java 1.7 or higher

How to build

$ ./

(ignore warning)

How to run

$ ./ < 001.graph


  • Yoichi Iwata
  • Kensuke Imanishi


Please cite the following two papers when you use our solver in your publication.

  • Yoichi Iwata, Magnus Wahlström, Yuichi Yoshida: Half-integrality, LP-branching, and FPT Algorithms. SIAM J. Comput. 45(4): 1377-1411 (2016)
  • Yoichi Iwata: Linear-Time Kernelization for Feedback Vertex Set. ICALP 2017: 68:1-68:14