Packing Strong Subgraph in Digraphs

TL;DR

This paper investigates two strong subgraph packing problems in directed graphs, establishing their computational complexity, inapproximability, and providing algorithmic solutions under certain structural constraints.

Contribution

It proves NP-completeness and inapproximability results for these problems and offers algorithms for specific digraph classes, advancing understanding of their computational complexity.

Findings

NP-completeness for symmetric and Eulerian digraphs

Inapproximability results for the packing problems

Algorithmic solutions for digraph compositions

Abstract

In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint strong subgraph packing problem and arc-disjoint strong subgraph packing problem. These problems can be viewed as generalizations of the famous Steiner tree packing problem and are closely related to the strong arc decomposition problem. We first prove the NP-completeness for the internally disjoint strong subgraph packing problem restricted to symmetric digraphs and Eulerian digraphs. Then we get inapproximability results for the arc-disjoint strong subgraph packing problem and the internally disjoint strong subgraph packing problem. Finally we study the arc-disjoint strong subgraph packing problem restricted to digraph compositions and obtain some algorithmic results by utilizing the structural properties.