Triangulation heuristics for maximum character compatibility

In this paper, we describe, to our knowledge, the first fast, accurate, triangulation-based heuristic solutions to the two-state maximum character compatibility problem with missing data. Recently, this problem has been reduced to a graph triangulation problem. Our first heuristic follows a classic approach from the triangulation literature, and our second heuristic is informed by the separation of monochromatic pairs. While slower, our informed heuristic generally performed better than our classic heuristic. We compared our heuristic solutions with optimal solutions obtained from minimal triangulation integer programs when possible, and were able to solve problems an order of magnitude larger using heuristics than were possible with this integer program.