Realizing Degree Sequences in Parallel

A sequence d of integers is a degree sequence if there exists a (simple) graph G such that the components of d are equal to the degrees of the vertices of G. The graph G is said to be a realization of d. We provide an efficient parallel algorithm to realize d; the algorithm runs in O(logn) time using O(n+m) CRCW PRAM processors, where n and m are the number of vertices and edges in G. Before our result, it was not known if the problem of realizing d is in NC.