On the Complexity of Point Recolouring in Geometric Graphs

Given a collection of points representing geographic data we consider the task of delineating boundaries based on the features of the points. Assuming that the features are binary, for example, red or blue, this can be viewed as determining red and blue regions, or states. Due to regional anomalies or sampling error, we may find that reclassifying, or recolouring, some points may lead to a more rational delineation of boundaries. In this note we study the maximal length of recolouring sequences where recolouring rules are based on neighbour relations and neighbours are defined by a geometric graph. We show that the difference in the maximal length of recolouring sequences is striking, as it can range from a linear bound for all trees, to an infinite sequence for some planar graphs.

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Henk Meijer, Yurai Núñez Rodríguez, David Rappaport
• Keywords: Blue Regions, CCCG 2008, Computational Geometry, Geographic Data, Maximal Length