Abstract
We develop a parallel algorithm for the domatic partition problem on interval graphs under the EREW PRAM model. Given a set of n intervals with their 2 n endpoints sorted, our algorithm takes O(log n)time and O( n/log n )processors. The cost (time-processor product) of our algorithm is O( n). Therefore our parallel algorithm is optimal. If these n intervals are not sorted, we can solve this problem in O(log n) time by using O( n) processors. This is optimal too. Our algorithm is based on some observations about the degrees of the intervals. These observations result in a very elegant parallel algorithm.
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