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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 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. Both of these algorithms are strongly polynomial. 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.
Bibtex entry:
AUTHOR | = | {Hujter, B{\'a}lint and Kiss, Viktor and T{\'o}thm{\'e}r{\'e}sz, Lilla}, |
TITLE | = | {On the complexity of the chip-firing reachability problem}, |
NOTE | = | {{\tt egres.elte.hu}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2015}, |
NUMBER | = | {TR-2015-10} |