Generalized map coloring for use in Geographical Information Systems

Abstract

We propose a new model for cartographic map coloring for use in Geographical Information Systems. Map coloring motivated the famous four-color problem in Mathematics. The published proofs of the four-color theorem yield impractical polynomial-time algorithms. Actual political maps often require generalizations to the standard four-coloring problem given the topology of some regions. We allow each region to have m disjoint pieces, which is Heawood's m-pire problem. We also count node adjacency between regions, i.e., two regions are adjacent if they share a common point. The adjacency graphs using node adjacency are known as map graphs. By combining m-pires with node and island adjacency, we formulate a new model to handle actual GIS instances. We implemented Brélaz's Dsatur heuristic, since no specific algorithm exists for coloring our resulting cartographic graphs. The choice works well in practice and we discuss the details of the implementation in TransCAD®.