Tight Bounds for Point Recolouring

In their paper on delineating boundaries from geographic data, Reinbacher et al. [9] use a recolouring method to reclassify points so that the boundaries that separate points of different colours become more reasonable. They show that an iterative recolouring method converges after a finite, but exponential, number of steps. They also give, as an example, a triangulated point set with a specified re-colouring sequence that uses (n2 ) recolourings. In this note we revisit this recolouring problem and obtain a matching O(n2 ) upper bound.

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Yurai Núñez Rodríguez, David Rappaport
• Keywords: CCCG 2006, CCCG 2007, Geographic Data, Iterative Recolouring Method, Recolouring Method