Algorithms for Euclidean Degree Bounded Spanning Tree Problems

TL;DR

This paper compares heuristic and approximation algorithms for Euclidean degree-bounded spanning tree problems, introduces new heuristics, and presents a novel edge swap algorithm that outperforms existing methods.

Contribution

The paper develops new heuristics and a novel edge swap algorithm for Euclidean degree-bounded spanning trees, demonstrating superior performance over existing algorithms.

Findings

The new edge swap algorithm outperforms all tested algorithms.

Heuristics show competitive accuracy for both problems.

Computational experiments validate the effectiveness of the proposed methods.

Abstract

Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the sum of the total length of its edges is minimum. Similarly, the Euclidean \textit{$\delta$-minimum bottleneck spanning tree} ($\delta$-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 $\delta \leq 4$, 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.