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Annals of Combinatorics

, Volume 19, Issue 2, pp 373–396 | Cite as

Feedback Arc Set Problem and NP-Hardness of Minimum Recurrent Configuration Problem of Chip-Firing Game on Directed Graphs

  • Kévin Perrot
  • Trung Van Pham
Article

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

chip-firing game critical configuration recurrent configuration Eulerian digraph feedback arc set complexity sandpile model 

Mathematics Subject Classification

68R10 90C27 05C20 05C45 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Departamento de Ingeniería MatemáticaUniversidad de Chile, CMM (UMI 2807 - CNRS)Blanco EncaldaChile
  2. 2.Aix Marseille UniversitéCNRSMarseilleFrance
  3. 3.Department of Mathematics for Computer ScienceInstitute of Mathematics, VASTHanoiVietnam

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