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 (https://pacechallenge.wordpress.com/track-b-feedback-vertex-set/). Preliminary results against the public data set: result.tsv

Implemented algorithms

• Linear-time kernel (http://arxiv.org/abs/1608.01463) (ReductionRoot.java)
  • 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 (HalfIntegralRelax.java)
    • + several heuristic reductions (these reductions are correct but would not improve the theoretical worst-case perfomance)
• FPT branch-and-bound (http://arxiv.org/abs/1310.2841) (FPTBranchingSolver.java)
  • This algorithm runs in O^*(4^k) time.
  • At each node of the search tree, we apply the following set of reductions (Reduction.java)
    • 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 (LowerBound.java)

Required

Java 1.7 or higher

How to build

$ ./build.sh

(ignore warning)

How to run

$ ./run.sh < 001.graph

Authors

• Yoichi Iwata
• Kensuke Imanishi

Citation

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