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Order Reconfiguration Under Width Constraints

Authors Emmanuel Arrighi , Henning Fernau , Mateus de Oliveira Oliveira , Petra Wolf

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Emmanuel Arrighi
  • University of Bergen, Norway
Henning Fernau
  • University of Trier, Germany
Mateus de Oliveira Oliveira
  • University of Bergen, Norway
Petra Wolf
  • University of Trier, Germany

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Emmanuel Arrighi, Henning Fernau, Mateus de Oliveira Oliveira, and Petra Wolf. Order Reconfiguration Under Width Constraints. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 8:1-8:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


In this work, we consider the following order reconfiguration problem: Given a graph G together with linear orders ω and ω' of the vertices of G, can one transform ω into ω' by a sequence of swaps of adjacent elements in such a way that at each time step the resulting linear order has cutwidth (pathwidth) at most k? We show that this problem always has an affirmative answer when the input linear orders ω and ω' have cutwidth (pathwidth) at most k/2. Using this result, we establish a connection between two apparently unrelated problems: the reachability problem for two-letter string rewriting systems and the graph isomorphism problem for graphs of bounded cutwidth. This opens an avenue for the study of the famous graph isomorphism problem using techniques from term rewriting theory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Mathematics of computing → Combinatorial optimization
  • Theory of computation → Equational logic and rewriting
  • Parameterized Complexity
  • Order Reconfiguration
  • String Rewriting Systems


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