Algorithms for degree-constrained Euclidean Steiner minimal tree

Abstract

A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree, it is also NP-hard. Two intelligent algorithms are proposed in an attempt to solve this difficult problem. Series of numerical examples are tested, which demonstrate that the algorithms also work well in practice.