Approximating Vertex Cover using Structural Rounding

TL;DR

This paper evaluates the structural rounding framework for approximating Vertex Cover by editing graphs to bipartite structures, demonstrating significant improvements over standard methods through new lifting strategies.

Contribution

It introduces new lifting strategies within the structural rounding framework for Vertex Cover and provides the first practical evaluation of this approach.

Findings

Structural rounding outperforms standard 2-approximations.

Simpler lifting strategies are highly effective.

Open-source implementation enables reproducibility.

Abstract

In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms. Structural rounding works by first editing to a well-structured class, efficiently solving the edited instance, and "lifting" the partial solution to recover an approximation on the input. We focus on the well-studied Vertex Cover problem, and edit to the class of bipartite graphs (where Vertex Cover has an exact polynomial time algorithm). In addition to the naive lifting strategy for Vertex Cover described by Demaine et al., we introduce a suite of new lifting strategies and measure their effectiveness on a large corpus of synthetic graphs. We find that in this setting, structural rounding significantly outperforms standard 2-approximations. Further, simpler lifting strategies are extremely competitive with the more sophisticated approaches. The implementations are available as an open-source Python package, and all experiments are replicable.