Feedback arc set problem and NP-hardness of minimum recurrent configuration problem of Chip-firing game on directed graphs
Computational Complexity
2015-06-05 v5 Discrete Mathematics
Combinatorics
Abstract
In this paper we present further studies of recurrent configurations of Chip-firing games on Eulerian directed graphs (simple digraphs), a class on the way from undirected graphs to general directed graphs. A computational problem that arises naturally from this model is to find the minimum number of chips of a recurrent configuration, which we call the minimum recurrent configuration (MINREC) problem. We point out a close relationship between MINREC and the minimum feedback arc set (MINFAS) problem on Eulerian directed graphs, and prove that both problems are NP-hard.
Keywords
Cite
@article{arxiv.1303.3708,
title = {Feedback arc set problem and NP-hardness of minimum recurrent configuration problem of Chip-firing game on directed graphs},
author = {Kévin Perrot and Trung Van Pham},
journal= {arXiv preprint arXiv:1303.3708},
year = {2015}
}
Comments
18 pages, 6 figures