Special Cases of the Minimum Spanning Tree Problem under Explorable Edge and Vertex Uncertainty

TL;DR

This paper investigates the Minimum Spanning Tree Problem with uncertain edges and vertices, focusing on special graph types like cactus graphs, and introduces complexity results for a related spanning star problem.

Contribution

It provides randomized algorithms for specific instances and demonstrates the difficulty of approximating a minimum weight spanning star under uncertainty.

Findings

Randomized algorithms for cactus graphs

No constant competitive ratio for the spanning star problem

Analysis of special instance types under uncertainty

Abstract

This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we provide randomized algorithms. We introduce the problem of finding a minimum weight spanning star under uncertainty for which we show that no algorithm can achieve constant competitive ratio.