Let H =< V, S > be a hypergraph, where V is a set of vertices and S is a set of not necessarily disjoint clusters Si ⊆ V. The Clustered Spanning Tree problem is to find a spanning tree of G which satisfies that each cluster induces a subtree, when it exists. We provide an efficient and unique algorithm which finds a feasible solution tree for H when it exists, or states that no feasible solution exists. The paper also uses special structures of the intersection graph of H to construct a feasible solution more efficiently. For cases when the hypergraph does not have a feasible solution tree, we consider adding vertices to exactly one cluster in order to gain feasibility. We characterize when such addition can gain feasibility, find the appropriate cluster and a possible set of vertices to be added.

Source : oai:HAL:hal-01887552v4

Volume: vol. 21 no. 1, ICGT 2018

Published on: August 27, 2019

Submitted on: October 22, 2018

Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]