Fast sequential and randomised parallel algorithms for rigidity and approximate min k-cut

Abstract

In this paper we use new techniques based on flows and matroid theory to produce fast sequential and randomised parallel algorithms for two important classes of problems. The first class arises in the study of rigidity of graphs (also in the study of graph realizations). The second class of problems may be called Principal Partition related problems. We take a representative of this class, viz, the rain k-cut problem and produce an RNC algorithm which solves this NP-hard problem within twice the optimal.