In this paper we consider the 2-layer constrained via minimization problem and the SNP haplotype assembly problem. The former problem arises in the design of integrated and printed circuit boards, and the latter comes up in the DNA sequencing process for diploid organisms. We show that, for any maximum junction degree, the problem can be reduced to the maximum bipartite induced subgraph problem. Moreover we show that the SNP haplotype assembly problem can also be reduced to the maximum bipartite induced subgraph problem for the so-called minimum error correction criterion. We give a partial characterization of the bipartite induced subgraph polytope. Using this, we devise a branch-and-cut algorithm and report some experimental results. This algorithm has been used to solve real and large instances.