Minimum‐Displacement Overlap Removal for Geo‐referenced Data Visualization

Abstract

Given a set of rectangles embedded in the plane, we consider the problem of adjusting the layout to remove all overlap while preserving the orthogonal order of the rectangles. The objective is to minimize the displacement of the rectangles. We call this problem Minimum-Displacement Overlap Removal (mdor). Our interest in this problem is motivated by the application of displaying metadata of archaeological sites. Because most existing overlap removal algorithms are not designed to minimize displacement while preserving orthogonal order, we present and compare several approaches which are tailored to our particular usecase. We introduce a new overlap removal heuristic which we call reArrange. Although conceptually simple, it is very effective in removing the overlap while keeping the displacement small. Furthermore, we propose an additional procedure to repair the orthogonal order after every iteration, with which we extend both our new heuristic and PRISM, a widely used overlap removal algorithm. We compare the performance of both approaches with and without this order repair method. The experimental results indicate that reArrange is very effective for heterogeneous input data where the overlap is concentrated in few dense regions.

Efficient Optimal Overlap Removal: Algorithms and Experiments

“…The removal of overlap between nodes finds also numerous applications in other visualization problems, such as visualizing disjoint glyphs on a map [vGPNB17], computing network layouts [DMS05, MSTH03], positioning nonspatial data [SSS*12, GNCNT13] and computing Demer's and Dorling cartograms [Dor96]. However, this problem of overlap removal is NP‐hard in most settings, leading to a wealth of heuristic approaches.…”

“…We use the centers of the symbols to decide this order. This constraint helps retain spatial relations, that may be crucial for certain application domains [vGPNB17].…”