Assessing the Computational Complexity of Multi-Layer Subgraph Detection

TL;DR

This paper explores the computational difficulty of detecting various subgraphs in multi-layer graphs, identifying which problems are hard or tractable, with implications for real-world network analysis.

Contribution

It systematically analyzes the complexity of subgraph detection problems in multi-layer graphs, highlighting both hardness results and specific cases of tractability.

Findings

Most problems are computationally hard even with few layers

Some subgraph detection problems are tractable under certain conditions

The study maps the boundary between tractable and intractable cases

Abstract

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multi-layer graphs, including fundamental problems such as maximum matching, finding certain clique relaxations (motivated by community detection), or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of tractability.