A Note on the Practicality of Maximal Planar Subgraph Algorithms

TL;DR

This paper compares various algorithms for the NP-hard Maximum Planar Subgraph problem, evaluating their practical performance, solution quality, and implementation complexity, revealing surprising insights about their relative strengths.

Contribution

It provides the first comprehensive practical comparison of heuristic, approximative, and exact algorithms for MPS, highlighting the effectiveness of a theoretically strong approximation in practice.

Findings

The approximation algorithm performs competitively in practice.

No single approach dominates across all metrics.

Implementation complexity varies significantly among methods.

Abstract

Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the best of our knowledge---they have never been compared competitively in practice. We report on an exploratory study on the relative merits of the diverse approaches, focusing on practical runtime, solution quality, and implementation complexity. Surprisingly, a seemingly only theoretically strong approximation forms the building block of the strongest choice.