Removing randomness in parallel computation without a processor penalty

Some general techniques are developed for removing randomness from randomized NC algorithms without a blowup in the number of processors. One of the requirements for the application of these techniques is that the analysis of the randomized algorithm uses only pairwise independence. The main new result is a parallel algorithm for the Delta +1 vertex coloring problem with running time O(log/sup 3/ nlog log n) using a linear number of processors on a concurrent-read-concurrent-write parallel random-access machine. The techniques also apply to several other problems, including the maximal-independent-set problem and the maximal-matching problem. The application of the general technique to these last two problems is mostly of academic interest, because NC algorithms using a linear number of processors that have better running times have been previously found.<>