Aleksandra Istomina | Searcharxiv

arXiv2023

Fine-grained reductions around CFL-reachability

In this paper we study the fine-grained complexity of the CFL reachability problem. We first present one of the existing algorithms for the problem and an overview of conditional lower bounds based on widely believed hypotheses. We then use the existing reduction techniques to obtain new conditional lower bounds on CFL reachability and related problems. We also devise a faster algorithm for the problem in case of bounded path lengths and a technique that may be useful in finding new conditional lower bounds.

cs.CC↗

arXiv2021

Morphing tree drawings in a small 3D grid

We study crossing-free grid morphs for planar tree drawings using 3D. A morph consists of morphing steps, where vertices move simultaneously along straight-line trajectories at constant speeds. A crossing-free morph is known between two drawings of an $n$-vertex planar graph $G$ with $\mathcal{O}(n)$ morphing steps and using the third dimension it can be reduced to $\mathcal{O}(\log n)$ for an $n$-vertex tree [Arseneva et al.\ 2019]. However, these morphs do not bound one practical parameter, the resolution. Can the number of steps be reduced substantially by using the third dimension while keeping the resolution bounded throughout the morph? We answer this question in an affirmative and present a 3D non-crossing morph between two planar grid drawings of an $n$-vertex tree in $\mathcal{O}(\sqrt{n} \log n)$ morphing steps. Each intermediate drawing lies in a $3D$ grid of polynomial volume.

cs.CG↗