A Practical Torus Embedding Algorithm and Its Implementation

Embedding graphs on the torus is a problem with both theoretical and practical significance. It is required to embed a graph on the torus for solving many application problems in graphs. Such problems appear in disciplines including VLSI design and graph drawing. Although polynomial time algorithms for embedding graphs on the torus exist, they are complex and no working implementation exists. To develop a practical tool for embedding graphs on the torus, we propose a new algorithm with exponential running time. Compared with a previous well known exponential time algorithm, our algorithm has better practical performance. Furthermore, we show that our implementation covers most modules of a polynomial time algorithm and can serve as a good foundation for its implementation.