Efficient approximation algorithms for domatic partition and on-line coloring of circular arc graphs

Exploits the close relationship between circular arc graphs and interval graphs to design efficient approximation algorithms for NP-hard optimization problems on circular arc graphs. The problems considered are maximum domatic partition and online minimum vertex coloring. We present a heuristic for the domatic partition problem with a performance ratio of 4. For online coloring, we consider two different online models. In the first model, arcs are presented in the increasing order of their left endpoints. For this model, our heuristic guarantees a solution which is within a factor of 2 of the optimal (off-line) value; and we show that no online coloring algorithm can achieve a performance guarantee of less than 3/2. In the second online model, arcs are presented in an arbitrary order; and it is known that no online coloring algorithm can achieve a performance guarantee of less than 3. For this model, we present a heuristic which provides a performance guarantee of 4