A Practical Algorithm for the Computation of the Genus

TL;DR

This paper presents a practical, efficient algorithm for computing the genus of a graph, emphasizing real-world performance over theoretical complexity, and demonstrating its effectiveness through implementation results.

Contribution

The paper introduces a new practical algorithm for graph genus computation and showcases its implementation and performance comparison with existing methods.

Findings

The algorithm is faster for many applications than previous methods.

Implementation results demonstrate competitive performance.

Design principles for backtracking algorithms are effectively applied.

Abstract

We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms. The aim of this algorithm is to be fast enough for many applications instead of focusing on the theoretical asymptotic complexity. Apart from the specific problem and the results, the article can also be seen as an example how some design principles used to carefully develop and implement standard backtracking algorithms can still result in very competitive programs.