Implicit Enumeration of Topological-Minor-Embeddings and Its Application to Planar Subgraph Enumeration

TL;DR

This paper introduces a decision diagram-based method for implicitly enumerating topological-minor-embeddings in graphs, significantly improving the efficiency of finding specific subgraphs like planar graphs.

Contribution

The paper presents a novel decision diagram approach for implicit enumeration of topological-minor-embeddings, enabling faster detection of planar and related subgraphs.

Findings

Method finds all planar subgraphs up to five orders of magnitude faster.

Applicable to enumerating subgraphs with forbidden topological minors.

Effective for various classes like outerplanar, series-parallel, and cactus subgraphs.

Abstract

Given graphs $G$ and $H$, we propose a method to implicitly enumerate topological-minor-embeddings of $H$ in $G$ using decision diagrams. We show a useful application of our method to enumerating subgraphs characterized by forbidden topological minors, that is, planar, outerplanar, series-parallel, and cactus subgraphs. Computational experiments show that our method can find all planar subgraphs in a given graph at most five orders of magnitude faster than a naive backtracking-based method.