On parallel complexity of maximum f-matching and the degree sequence problem

Abstract

We present a randomized NC solution to the problem of constructing a maximum (cardinality) f-matching. As a corollary, we obtain a randomized NC algorithm for the problem of constructing a graph satisfying a sequence d1, d2,..., dn of equality degree constraints. We provide an optimal NC algorithm for the decision version of the degree sequence problem and an approximation NC algorithm for the construction version of this problem. Our main result is an NC algorithm for constructing if possible a graph satisfying the degree constraints d1, d2,..., dn in case di ≤ {Formula present} dj/5 for i=1, ..., n.