Degree-bounded minimum spanning trees

A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees

A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees

A Approximating Minimum Bounded Degree Spanning Trees to within One of Optimal

In the Minimum Bounded Degree Spanning Tree problem, we are given an undirected graph G = (V,E) with a degree upper bound Bv on each vertex v ∈ V , and the task is to find a spanning tree of minimum cost that satisfies all the degree bounds. Let OPT be the cost of an optimal solution to this problem. In this paper, we present a polynomial time algorithm which returns a spanning tree T of cost a...

Proximity Drawings of High-Degree Trees

A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the p...

Approximation of the Degree-Constrained Minimum Spanning Hierarchies

Degree-bounded spanning problems are well known and are mainly used to solve capacity constrained communication (routing) problems. The degree-constrained spanning tree problems are NP-hard and the minimum cost spanning tree is not approximable nor in the case where the entire graph must be spanned neither in partial spanning problems. Most of applications (such as communications) do not need t...