In the maximum sharing problem (MS), we want to compute a set of (non-simple) paths in an undirected bipartite graph covering as many nodes as possible of the first layer of the graph, with the constraint that all paths have both endpoints in the second layer and no node in that layer is covered more than once. MS is equivalent to the node-duplication based crossing elimination problem (NDCE) that arises in the design of molecular quantum-dot cellular automata (QCA) circuits and the physical synthesis of BDD based regular circuit
Amitabh Chaudhary, Danny Z. Chen, Rudolf Fleischer