2026-08-07T12:10:52Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23440 2025-10-02T12:55:12Z ddc:004 open_access

Computing Distances on Graph Associahedra Is Fixed-Parameter Tractable Cunha, Luís Felipe I. Sau, Ignasi Souza, Uéverton S. Valencia-Pabon, Mario graph associahedra elimination tree rotation distance parameterized complexity fixed-parameter tractable algorithm combinatorial shortest path reconfiguration An elimination tree of a connected graph G is a rooted tree on the vertices of G obtained by choosing a root v and recursing on the connected components of G-v to obtain the subtrees of v. The graph associahedron of G is a polytope whose vertices correspond to elimination trees of G and whose edges correspond to tree rotations, a natural operation between elimination trees. These objects generalize associahedra, which correspond to the case where G is a path. Ito et al. [ICALP 2023] recently proved that the problem of computing distances on graph associahedra is NP-hard. In this paper we prove that the problem, for a general graph G, is fixed-parameter tractable parameterized by the distance k. Prior to our work, only the case where G is a path was known to be fixed-parameter tractable. To prove our result, we use a novel approach based on a marking scheme that restricts the search to a set of vertices whose size is bounded by a (large) function of k. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Luís Felipe I. Cunha and Ignasi Sau and Uéverton S. Souza and Mario Valencia-Pabon 2025 Is Part Of LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2025.63 urn:nbn:de:0030-drops-234408 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.63 eng https://creativecommons.org/licenses/by/4.0/legalcode