Jack Edmonds

Jack R. Edmonds (born April 5, 1934) is an American computer scientist, regarded as one of the most important contributors to the field of combinatorial optimization. He was the recipient of the 1985 John von Neumann Theory Prize.

Research

A break through contribution of Edmonds is defining the concept of polynomial time characterising the difference between a practical and an impractical algorithm. Another of Edmonds' earliest and most notable contributions is the blossom algorithm for constructing maximum matchings on graphs, discovered in 1961, and published in 1965. This was the first polynomial-time algorithm for maximum matching in graphs. Its generalization to weighted graphs was a conceptual breakthrough in the usage of linear programming ideas in combinatorial optimization. It sealed in the importance of there being proofs/witnesses that the answer for an instance is yes and there being proofs/witnesses that the answer for an instance is no.

Additional landmark work of Edmonds is in the area of matroids. He found a polyhedral description for all spanning trees of a graph, and more generally for all independent sets of a matroid. Building on this, as a novel application of linear programming to discrete mathematics, he proved the matroid intersection theorem, a very general min-max combinatorial theorem which, in modern terms, showed that the matroid intersection problem lay in both NP and co-NP.