Schematic Representation of Large Biconnected Graphs

TL;DR

This paper explores schematic representations of large biconnected graphs with a main component and smaller separated components, proposing polynomial-time algorithms for their existence based on constrained book-embeddings.

Contribution

It introduces a new approach to visualize complex biconnected graphs using schematic drawings and provides algorithms to test their existence efficiently.

Findings

Polynomial-time algorithms for schematic representation existence

Mapping to constrained 1-page book-embeddings

Multiple drawing conventions considered

Abstract

Suppose that a biconnected graph is given, consisting of a large component plus several other smaller components, each separated from the main component by a separation pair. We investigate the existence and the computation time of schematic representations of the structure of such a graph where the main component is drawn as a disk, the vertices that take part in separation pairs are points on the boundary of the disk, and the small components are placed outside the disk and are represented as non-intersecting lunes connecting their separation pairs. We consider several drawing conventions for such schematic representations, according to different ways to account for the size of the small components. We map the problem of testing for the existence of such representations to the one of testing for the existence of suitably constrained $1$-page book-embeddings and propose several polynomial-time algorithms.