AN EFFICIENT PARALLEL ALGORITHM FOR COMPUTING A LARGE INDEPENDENT SET IN A PLANAR GRAPH

Let alpha(G) denote the independence number of a graph G, that is the maximum number of pairwise independent vertices in G. We present a parallel algorithm that computes in a planar graph G = (V, E), an independent set I is contained in or equal to V such that \I\ greater-than-or-equal-to alpha(G)/2. The algorithm runs in time O(log2 n) and requires a linear number of processors. This is achieved by defining a new set of reductions that can be executed "locally" and simultaneously; furthermore, it is shown that a constant fraction of the vertices in the graph are reducible. This is the best known approximation scheme when the number of processors available is linear; parallel implementation of known sequential algorithms requires many more processors.