Order Reconfiguration Under Width Constraints
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.
Parameterized Complexity
Order Reconfiguration
String Rewriting Systems
Theory of computation~Fixed parameter tractability
Mathematics of computing~Combinatorial optimization
Theory of computation~Equational logic and rewriting
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Regular Paper
Emmanuel
Arrighi
Emmanuel Arrighi
University of Bergen, Norway
https://orcid.org/0000-0002-0326-1893
Research Council of Norway (274526), IS-DAAD (309319).
Henning
Fernau
Henning Fernau
University of Trier, Germany
https://orcid.org/0000-0002-4444-3220
DAAD PPP (57525246).
Mateus
de Oliveira Oliveira
Mateus de Oliveira Oliveira
University of Bergen, Norway
https://orcid.org/0000-0001-7798-7446
Research Council of Norway (288761), IS-DAAD (309319).
Petra
Wolf
Petra Wolf
University of Trier, Germany
https://www.wolfp.net/
https://orcid.org/0000-0003-3097-3906
DFG project FE 560/9-1, DAAD PPP (57525246).
10.4230/LIPIcs.MFCS.2021.8
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Emmanuel Arrighi, Henning Fernau, Mateus de Oliveira Oliveira, and Petra Wolf
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