Parameterized Algorithms for Upward Planarity

TL;DR

This paper introduces new parameterized algorithms for testing upward planarity in directed acyclic graphs, utilizing a novel framework that combines SPQR tree-decompositions with parameterized techniques, advancing previous results.

Contribution

It presents three new fixed-parameter and XP-algorithms for upward planarity, unifying and extending prior tractability results using a novel decomposition-based framework.

Findings

Algorithms for upward planarity with fixed parameters

Extension of tractability to broader graph classes

Unified framework combining SPQR trees with parameterized methods

Abstract

We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an XP-algorithm parameterized by treewidth, and a fixed-parameter algorithm parameterized by treedepth. All three algorithms are obtained using a novel framework for the problem that combines SPQR tree-decompositions with parameterized techniques. Our approach unifies and pushes beyond previous tractability results for the problem on series-parallel digraphs, single-source digraphs and outerplanar digraphs.