The Least-Dependency Constrained Spanning Tree Problem

  • Luiz Alberto Viana UFC
  • Manoel Campêlo UFC

Resumo


We introduce the Least-Dependency Constrained Spanning Tree Problem, which consists of finding a spanning tree where each edge has at least one edge of its dependency set, if non-empty, also in the tree. The dependencies on the input graph G are described by a digraph D where the vertices are the edges of G, and the in-neighbors of a vertex are its dependency set. We show that the optimization problem is NP-hard even if G is a chordal cactus with maximum degree 3 or diameter at most 2, and D is a disjoint union of arborescences of height 2. The same complexity is proved when G is planar bipartite, and each component of D is an oriented cycle or an anti-arborescence of height 1. We also report two polynomial cases.

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Publicado
02/07/2017
VIANA, Luiz Alberto; CAMPÊLO, Manoel. The Least-Dependency Constrained Spanning Tree Problem. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 2. , 2017, São Paulo. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2017 . p. 53-56. ISSN 2595-6116. DOI: https://doi.org/10.5753/etc.2017.3190.