2025/04/25 by Cunha, Luís Felipe I., Sau, Ignasi, Souza, Uéverton S. +1
#05C10 #05C85 #0C05 #90C08 #90C27 #Combinatorics (math.CO) #Computational Geometry (cs.CG) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2.1 #G.2.2 #G.2.3
paper · doi:10.48550/arxiv.2504.18338
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.