Quantum Graph Drawing

TL;DR

This paper explores quantum algorithms for graph drawing problems, applying quantum circuit and annealing models to achieve speedups and demonstrate competitiveness in crossing minimization tasks.

Contribution

It introduces quantum algorithms for fundamental graph drawing problems, providing a framework for potential quantum speedups and experimental validation with quantum annealing.

Findings

Quadratic speedup using Grover's search in quantum circuits.

Quantum annealing shows competitive performance on crossing minimization.

Framework applicable to various graph drawing optimization problems.

Abstract

In this paper, we initiate the study of quantum algorithms in the Graph Drawing research area. We focus on two foundational drawing standards: 2-level drawings and book layouts. Concerning $2$-level drawings, we consider the problems of obtaining drawings with the minimum number of crossings, $k$-planar drawings, quasi-planar drawings, and the problem of removing the minimum number of edges to obtain a $2$-level planar graph. Concerning book layouts, we consider the problems of obtaining $1$-page book layouts with the minimum number of crossings, book embeddings with the minimum number of pages, and the problem of removing the minimum number of edges to obtain an outerplanar graph. We explore both the quantum circuit and the quantum annealing models of computation. In the quantum circuit model, we provide an algorithmic framework based on Grover's quantum search, which allows us to obtain, at least, a quadratic speedup on the best classical exact algorithms for all the considered problems. In the quantum annealing model, we perform experiments on the quantum processing unit provided by D-Wave, focusing on the classical $2$-level crossing minimization problem, demonstrating that quantum annealing is competitive with respect to classical algorithms.