Spanning caterpllars with bounded diameter

On Algorithm for the Minimum Spanning Trees Problem with Diameter Bounded Below

The minimum spanning trees problem is to find k edge-disjoint spanning trees in a given undirected weighted graph. It can be solved in polynomial time. In the k minimum spanning trees problem with diameter bounded below (k-MSTBB) there is an additional requirement: a diameter of every spanning tree must be not less than some predefined value d. The k-MSTBB is NP hard. We propose an asymptotical...

Encoding Bounded-Diameter Spanning Trees with Permutations and with Random Keys

Permutations of vertices can represent constrained spanning trees for evolutionary search via a decoder based on Prim’s algorithm, and random keys can represent permutations. Though we might expect that random keys, with an additional level of indirection, would provide inferior performance compared with permutations, a genetic algorithm that encodes spanning trees with random keys is as effect...

Variable Neighborhood Search for the Bounded Diameter Minimum Spanning Tree Problem

The bounded diameter minimum spanning tree problem is an NP-hard combinatorial optimization problem with applications in various fields like communication network design. We propose a general variable neighborhood search approach for it, utilizing four different types of neighborhoods. They were designed in a way enabling an efficient incremental evaluation and search for the best neighboring s...

A sharp threshold for minimum bounded-depth/diameter spanning and Steiner trees

In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to ζ(3) = 1/13 + 1/23 + 1/33 + · · · as n → ∞. We consider spanning trees constrained to have depth bounded by k from a specified root. We prove that if k ≥ log2 log n+ω(1), where ω(1) is any function going to ∞ with n, then th...

Cluster-Based (Meta-)Heuristics for the Euclidean Bounded Diameter Minimum Spanning Tree Problem