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In this paper we present an approach that combines the process of column encoding and input-output encoding. Traditionally, the process of column minimization is represented as a set covering or clique partitioning or graph coloring algorithms. These algorithms are well known NP-hard problems. The column minimization problem is followed by the input-output encoding problem, which is represented as a weighted graph assignment problem, which is again a well known NP-hard problem. The combined column minimization and input-output encoding algorithm reduces the complexity by representing both the above problems as a single weighted graph encoding problem. The proposed algorithm has been implemented and evaluated with standard benchmarks.