Approximation of the Degree-Constrained Minimum Spanning Hierarchies
Degree-constrained spanning problems are well known and are mainly used to solve capacity constrained routing problems. The degree-constrained spanning tree problems are NP-hard and computing the minimum cost spanning tree is not approximable. Often, applications (such as some degree-constrained communications) do not need trees as solutions. Recently, a more flexible, connected, graph related structure called hierarchy was proposed to span a set of vertices under constraints. This structure permits a new formulation of some degree-constrained spanning problems. In this paper we show that although the newly formulated problem is still NP-hard, it is approximable with a constant ratio. In the worst case, this ratio is bounded by 3/2. We provide a simple heuristic and prove its approximation ratio is the best possible for any algorithm based on a minimum spanning tree.
KeywordsGraph theory Networks Degree-Constrained Spanning Problem Spanning Hierarchy Approximation
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