2018/09/25 by Andersen, Patrick J., Ras, Charl J.
#90C27 #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1809.09348
Given a set of points in the Euclidean plane, the Euclidean δ-minimum spanning tree (δ-MST) problem is the problem of finding a spanning tree with maximum degree no more than δ for the set of points such the sum of the total length of its edges is minimum. Similarly, the Euclidean δ-minimum bottleneck spanning tree (δ-MBST) problem, is the problem of finding a degree-bounded spanning tree for a set of points in the plane such that the length of the longest edge is minimum. When δ≤ 4, these two problems may yield disjoint sets of optimal solutions for the same set of points. In this paper, we perform computational experiments to compare the accuracies of a variety of heuristic and approximation algorithms for both these problems. We develop heuristics for these problems and compare them with existing algorithms. We also describe a new type of edge swap algorithm for these problems that outperforms all the algorithms we tested.