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We present an efficient heuristic for finding good bipartitions of the vertex set of a graph in the sense of the well-known measure of ratioCut (essentially the ratio between weight of cut edges and the product of weights of the nodesets of the bipartition). The widely accepted ratioCut bipartitioning algorithm of Wei and Cheng is similar in spirit to the Fiduccia-Mattheyeses algorithm (F-M algorithm). Our approach makes use of F-M algorithm as the first phase that takes in as an input, random bipartitions. In the later phase of our algorithm we make use of a new coarsening strategy and follow it up with a submodular function optimization algorithm on the coarsened graph. We also present the comparison of results of this approach applied to benchmark circuits with the well-established algorithms such as the Wei-Cheng algorithm for ratioCut bipartitioning and pmetis of Metis package. The comparative study not only shows that this new approach indeed produces good quality ratioCut bipartitions, but also the fact that this approach has the potential of finding a large number of such good partitions in comparison with other approaches. The key subroutine in our heuristic strategies is based on the recent finding about the role of submodular functions in designing new heuristics and approximate algorithms to some NP-hard problems.