Graph folding and programmable logic array

The problem of compacting a programmable logic array is formulated as the following graph problem. Given a red-edge bipartite graph, how to add maximum number of independent green edges such that there are no cycles formed by alternating red and green edges. For this NP-complete problem, we present a polynomial heuristic algorithm which gives an optimum solution when the red bipartite graph satisfies certain conditions, e.g., a tree. When the bipartite graph does not satisfy these conditions, the heuristic algorithm gives a solution with worst-case error bound. For a red bipartite graph with given cardinality, we give a tight upper bound on the number of green edges.