Degree-Constrained Minimum Spanning Hierarchies in Graphs

Abstract

The minimum spanning tree problem in graphs under budget-type degree constraints (DCMST) is a well-known NP-hard problem. Spanning trees do not always exist, and the optimum can not be approximated within a constant factor. Recently, solutions have been proposed to solve degree-constrained spanning problems in the case of limited momentary capacities of the nodes. For a given node, the constraint represents a limited degree of the node for each visit. Finding the solution with minimum cost is NP-hard and the related algorithms are not trivial. This paper focuses on this new spanning problem with heterogeneous capacity-like degree bounds. The minimum cost solution corresponds to a graph-related structure, i.e., a hierarchy. We study the conditions of its existence, and we propose its exact computation, a heuristic algorithm, and its approximation.

Keywords

• graph theory
• degree constrained spanning trees
• spanning hierarchies
• homomorphism
• NP-hard problem
• exact computation