On the Minimum Spanning Tree for Directed Graphs with Potential Weights

TL;DR

This paper investigates conditions under which minimum spanning trees in directed graphs with potential weights can be found using algorithms designed for undirected graphs, simplifying the problem under certain weight conditions.

Contribution

It identifies specific weight conditions that make the directed MST problem equivalent to the undirected case, enabling simpler algorithms.

Findings

Identifies weight conditions for equivalence between directed and undirected MSTs.

Provides criteria for when undirected algorithms can be applied to directed graphs.

Simplifies the solution process for certain classes of directed MST problems.

Abstract

In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected graphs cannot usually be applied to the directed case. In this paper we examine the kind of weights such that the problems are equivalent and a minimum spanning tree of a directed graph may be found by a simple algorithm for an undirected graph.