Book drawing algorithm for fixed vertex order graph

Abstract

Book drawing is a type of graph embedding in which the vertices of a graph 𝐺 are placed along a straight line called the spine of a book, and the edges are assigned to the pages so that each page contains a subset of the edges. The main goal in book drawing is to minimize the number of pages required while keeping the number of crossings per edge bounded by a non-negative integer 𝑏. In this paper, we present a heuristic algorithm that produces a book drawing for any graph in polynomial time. The algorithm assigns rankings to the edges of the graph, and using these rankings along with the crossing bound as parameters, it generates the book drawing of the graph. We evaluate our algorithm through experiments on two types of graphs: randomly generated graphs using the Erd˝os–R´enyi model and randomly generated regular Hamiltonian graphs. In addition, we present results on several well-known graphs to show how our algorithm distributes the edges across pages under different crossing bounds.