An experimental study of algorithms for obtaining a singly connected subgraph

TL;DR

This paper investigates algorithms for finding minimal edge removals in directed acyclic graphs to ensure they are singly connected, providing polynomial-time solutions for specific graph types.

Contribution

It introduces algorithms for the minimal edge removal problem to achieve singly connected subgraphs and proves polynomial solvability for certain graph classes.

Findings

Algorithms for minimal edge removal are effective.

Polynomial-time solutions exist for specific graph types.

The problem is computationally tractable under certain conditions.

Abstract

A directed graph G = (V,E) is singly connected if for any two vertices v, u of V, the directed graph G contains at most one simple path from v to u. In this paper, we study different algorithms to find a feasible but necessarily optimal solution to the following problem. Given a directed acyclic graph G = (V, E), find a subset H of E of minimum size such that the subgraph (V, E-H) is singly connected. Moreover, we prove that this problem can be solved in polynomial time for a special kind of directed graphs.