Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

On the complexity of the chip-firing reachability problem


Authors: Bálint Hujter, Viktor Kiss and Lilla Tóthmérész
Journal: Proc. Amer. Math. Soc. 145 (2017), 3343-3356
MSC (2010): Primary 05C57, 05C50, 68Q25
DOI: https://doi.org/10.1090/proc/13498
Published electronically: February 15, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05C57, 05C50, 68Q25

Retrieve articles in all journals with MSC (2010): 05C57, 05C50, 68Q25


Additional Information

Bálint Hujter
Affiliation: MTA-ELTE Egerváry Research Group, Department of Operations Research, Eötvös Loránd University, Budapest, Hungary
Email: hujterb@cs.elte.hu

Viktor Kiss
Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Hungary
Email: kivi@cs.elte.hu

Lilla Tóthmérész
Affiliation: MTA-ELTE Egerváry Research Group, Department of Computer Science, Eötvös Loránd University, Budapest, Hungary
Email: tmlilla@cs.elte.hu

DOI: https://doi.org/10.1090/proc/13498
Keywords: Chip-firing game, computational complexity.
Received by editor(s): December 2, 2015
Received by editor(s) in revised form: September 21, 2016
Published electronically: February 15, 2017
Additional Notes: The first author was supported by the Hungarian Scientific Research Fund - OTKA K109240.
The second author was supported by the Hungarian Scientific Research Fund - OTKA 104178, 113047.
The third author was supported by the Hungarian Scientific Research Fund - OTKA K109240.
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2017 American Mathematical Society