Testing Upward Planarity of Partial $2$-Trees

TL;DR

This paper introduces an efficient $O(n^2)$ algorithm for testing upward planarity in directed partial 2-trees, significantly improving the computational complexity over previous methods.

Contribution

The paper presents the first $O(n^2)$-time algorithm for upward planarity testing specifically for directed partial 2-trees, enhancing efficiency.

Findings

Achieved $O(n^2)$ time complexity for the problem.

Improved upon the previous $O(n^4)$ algorithm.

Provides a practical method for upward planarity testing in specific graph classes.

Abstract

We present an $O(n^2)$-time algorithm to test whether an $n$-vertex directed partial $2$-tree is upward planar. This result improves upon the previously best known algorithm, which runs in $O(n^4)$ time.