Parallel PROFIT/COST algorithms through fast derandomization

Abstract.

We present parallel algorithms for the PROFIT/COST problem with time complexity $O(\log n)$ using O(m+n) processors. The design of these algorithms employ both the derandomization technique and the pipeline technique. They can be used to partition the vertices of a graph into two sets such that the number of edges incident with vertices in both sets is at least half of the total number of edges in the graph. Parallel algorithms for the PROFIT/COST problem have known applications in the design of parallel algorithms for several graph problems.