Johnson received a number of awards, including the following: The selection committee cited among Johnson's contribution three important and influential papers he produced in the early seventies—two of them with
Ralph Gomory—which developed and extended in significant ways the group theoretic approach to integer programming pioneered by Gomory. In particular, Johnson showed how the approach can be extended to the case of mixed integer programs. As an outgrowth of this work, Johnson contributed decisively to the development of what became known as the subadditive approach to integer programming. Still in the seventies, in a seminal paper co-authored with
Jack Edmonds, Johnson showed how several basic optimization problems defined on graphs can be solved in polynomial time by reducing them to weighted matching problems. One example is finding minimum T-joins (i.e., edge sets whose only endpoints of odd degree are those in a specified vertex set T). An important special case is the seemingly difficult problem of finding a shortest tour in a graph that traverses every edge at least once, known as the Postman problem. The stark contrast between the polynomial solvability of this problem and the intractability of the
traveling salesman problem in which the tour is supposed to traverse vertices rather than edges, helped focus attention on the phenomenon so typical of combinatorial structures: two seemingly very similar problems turn out in reality to be vastly different. ==References==