Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm

Simon D. Fink; Ignaz Rutter

Home/Archive/arXiv

arXiv · 2310.20632

Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm

Simon D. Fink·Ignaz Rutter

View original source ↗Read source document ↗Export metadata ↓

Abstract

In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level Planarity, where vertices have to lie on given horizontal lines indicating a hierarchy, and Clustered Planarity, where we additionally draw the boundaries of clusters which recursively group the vertices in a crossing-free manner. Despite receiving significant amount of attention and substantial theoretical progress on these problems, only very few of the found solutions have been put into practice and evaluated experimentally. In this paper, we describe our implementation of the recent quadratic-time algorithm by Bl\"asius et al. [TALG Vol 19, No 4] for solving the problem Synchronized Planarity, which can be seen as a common generalization of several constrained planarity problems, including the aforementioned ones. Our experimental evaluation on an existing benchmark set shows that even our baseline implementation outperforms all competitors by at least an order of magnitude. We systematically investigate the degrees of freedom in the implementation of the Synchronized Planarity algorithm for larger instances and propose several modifications that further improve the performance. Altogether, this allows us to solve instances with up to 100 vertices in milliseconds and instances with up to 100 000 vertices within a few minutes.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Simon D. Fink, Ignaz Rutter. 2023-10-31. Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm. https://arxiv.org/abs/2310.20632

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗