Implementing a Partitioned 2-page Book Embedding Testing Algorithm

TL;DR

This paper presents an efficient implementation and experimental validation of a linear-time algorithm for the Partitioned 2-page Book Embedding problem, with implications for clustered planarity testing.

Contribution

It provides a practical implementation of a complex theoretical algorithm for Partitioned 2-page Book Embedding and demonstrates its effectiveness through experiments.

Findings

Algorithm is efficient and practical for testing partitioned 2-page book embeddings.

Implementation successfully extends to clustered planarity testing with two clusters.

Experimental results confirm the algorithm's effectiveness in real-world scenarios.

Abstract

In a book embedding the vertices of a graph are placed on the "spine" of a "book" and the edges are assigned to "pages" so that edges on the same page do not cross. In the Partitioned 2-page Book Embedding problem egdes are partitioned into two sets E_1 and E_2, the pages are two, the edges of E_1 are assigned to page 1, and the edges of E_2 are assigned to page 2. The problem consists of checking if an ordering of the vertices exists along the spine so that the edges of each page do not cross. Hong and Nagamochi give an interesting and complex linear time algorithm for tackling Partitioned 2-page Book Embedding based on SPQR-trees. We show an efficient implementation of this algorithm and show its effectiveness by performing a number of experimental tests. Because of the relationships between Partitioned 2-page Book Embedding and clustered planarity we yield as a side effect an implementation of a clustered planarity testing where the graph has exactly two clusters.