English

On the complexity of the chip-firing reachability problem

Combinatorics 2017-05-23 v4

Abstract

In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial time, even if the digraph has multiple edges. We also show a special case when the reachability problem can be decided in polynomial time for general digraphs: if the target distribution is recurrent restricted to each strongly connected component. As a further positive result, we show that the chip-firing reachability problem is in co-NP for general digraphs. We also show that the chip-firing halting problem is in co-NP for Eulerian digraphs.

Keywords

Cite

@article{arxiv.1507.03209,
  title  = {On the complexity of the chip-firing reachability problem},
  author = {Bálint Hujter and Viktor Kiss and Lilla Tóthmérész},
  journal= {arXiv preprint arXiv:1507.03209},
  year   = {2017}
}