Fixed-Parameter Tractability of the (1+1) Evolutionary Algorithm on Random Planted Vertex Covers
<|reference_start|>Fixed-Parameter Tractability of the (1+1) Evolutionary Algorithm on Random Planted Vertex Covers: We present the first parameterized analysis of a standard (1+1) Evolutionary Algorithm on a distribution of vertex cover problems. We show that if the planted cover is at most logarithmic, restarting the (1+1) EA every $O(n \log n)$ steps will find a cover at least as small as the planted cover in polynomial time for sufficiently dense random graphs $p > 0.71$. For superlogarithmic planted covers, we prove that the (1+1) EA finds a solution in fixed-parameter tractable time in expectation.   We complement these theoretical investigations with a number of computational experiments that highlight the interplay between planted cover size, graph density and runtime.<|reference_end|>
@article{kearney2024fixed-parameter,
    title={Fixed-Parameter Tractability of the (1+1) Evolutionary Algorithm on
  Random Planted Vertex Covers},
    author={Jack Kearney and Frank Neumann and Andrew M. Sutton},
    journal={Proceedings of the 17th ACM/SIGEVO Conference on Foundations of
  Genetic Algorithms (FOGA 2023)},
    year={2024},
    doi={10.1145/3594805.3607134},
    archivePrefix={arXiv},
    eprint={2409.10144},
    primaryClass={cs.NE}
}