English

Steepest ascent can be exponential in bounded treewidth problems

Discrete Mathematics 2020-05-18 v2 Data Structures and Algorithms Neural and Evolutionary Computing Populations and Evolution

Abstract

We investigate the complexity of local search based on steepest ascent. We show that even when all variables have domains of size two and the underlying constraint graph of variable interactions has bounded treewidth (in our construction, treewidth 7), there are fitness landscapes for which an exponential number of steps may be required to reach a local optimum. This is an improvement on prior recursive constructions of long steepest ascents, which we prove to need constraint graphs of unbounded treewidth.

Keywords

Cite

@article{arxiv.1911.08600,
  title  = {Steepest ascent can be exponential in bounded treewidth problems},
  author = {David A. Cohen and Martin C. Cooper and Artem Kaznatcheev and Mark Wallace},
  journal= {arXiv preprint arXiv:1911.08600},
  year   = {2020}
}

Comments

8 pages main text, 4 pages appendix, 1 page references; fixed error in f(a,b) to match code

R2 v1 2026-06-23T12:21:37.354Z