Efficient Approximation Algorithms for Domatic Partition and On-Line Coloring of Circular Arc Graphs

We exploit 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 here are maximum domatic partition and on-line minimum vertex coloring. We present a heuristic for the domatic partition problem with a performance ratio of 4. For on-line coloring, we consider two different on-line 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 on-line 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 on-lane 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.