Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth

TL;DR

This paper studies crossing minimization in graph drawings with 1 or 2 pages, showing fixed-parameter tractability results for various related problems using Courcelle's theorem and properties of bounded treewidth.

Contribution

It establishes fixed-parameter tractability of crossing minimization problems for 1-page and 2-page drawings of graphs with bounded treewidth, using monadic second order logic.

Findings

1-page crossing number is fixed-parameter tractable.

Testing 2-page planarity is fixed-parameter tractable.

Computing 2-page crossing number is fixed-parameter tractable.

Abstract

We investigate crossing minimization for 1-page and 2-page book drawings. We show that computing the 1-page crossing number is fixed-parameter tractable with respect to the number of crossings, that testing 2-page planarity is fixed-parameter tractable with respect to treewidth, and that computing the 2-page crossing number is fixed-parameter tractable with respect to the sum of the number of crossings and the treewidth of the input graph. We prove these results via Courcelle's theorem on the fixed-parameter tractability of properties expressible in monadic second order logic for graphs of bounded treewidth.