Snapping Graph Drawings to the Grid Optimally

TL;DR

This paper studies the problem of snapping planar graph drawings to a grid while preserving their embedding, proving NP-hardness for various objectives and providing an ILP formulation for optimal grid placement.

Contribution

It introduces the first complexity results for grid snapping of planar graphs with fixed embedding and offers an ILP approach for optimal grid drawing.

Findings

NP-hardness results for multiple objectives

ILP formulation for grid drawing optimization

Method for minimal height grid placement

Abstract

In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space consumption as well as computation time. This process is called snapping to the grid and has been investigated thoroughly from a computational-geometry perspective. In this paper we investigate the same problem for given drawings of planar graphs under the restriction that their combinatorial embedding must be kept and edges are drawn straight-line. We show that the problem is NP-hard for several objectives and provide an integer linear programming formulation. Given a plane graph G and a positive integer w, our ILP can also be used to draw G straight-line on a grid of width w and minimum height (if possible).