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Papers by William Cunningham

Research paper thumbnail of Integral solutions of linear complementarity problems

Mathematics of operations research, 1998

Research paper thumbnail of Integral solutions of linear complementarity problems

Mathematics of operations research, 1998

Research paper thumbnail of Ladders for Travelling Salesmen

SIAM Journal on Optimization, 1995

Research paper thumbnail of Converting Linear Programs to Network Problems

Mathematics of Operations Research, Aug 1, 1980

Research paper thumbnail of Integrality of Polyhedra

Research paper thumbnail of A primal algorithm for optimum matching

Mathematical Programming

An algorithm for finding an optimum weight perfect matching in a graph is described. It differs f... more An algorithm for finding an optimum weight perfect matching in a graph is described. It differs from Edmonds’ “blossom” algorithm in that a perfect matching is at hand throughout the algorithm, and a feasible solution to the dual problem is obtained only at termination. In many other respects, including its efficiency, it is similar to the blossom algorithm. Some advantages of this “primal” algorithm for certain post-optimality problems are described. The algorithm is used to prove that, if the weights are integers, then the dual problem has an optimal solution which is integer-valued. Finally, some graph-theoretic results on perfect matchings are derived.

Research paper thumbnail of On theorems of berge and fournier

Research paper thumbnail of On submodular function minimization

Research paper thumbnail of An algorithm for packing non-zero A-paths in group-labelled graphs

Research paper thumbnail of The optimal path-matching problem

Research paper thumbnail of Principally Unimodular Skew-Symmetric Matrices

Research paper thumbnail of Delta-Matroids, Jump Systems, Bisubmodular Polyhedra

Siam Journal on Discrete Mathematics, 1995

Research paper thumbnail of Integral solutions of linear complementarity problems

Mathematics of operations research, 1998

Research paper thumbnail of Integral solutions of linear complementarity problems

Mathematics of operations research, 1998

Research paper thumbnail of Ladders for Travelling Salesmen

SIAM Journal on Optimization, 1995

Research paper thumbnail of Converting Linear Programs to Network Problems

Mathematics of Operations Research, Aug 1, 1980

Research paper thumbnail of Integrality of Polyhedra

Research paper thumbnail of A primal algorithm for optimum matching

Mathematical Programming

An algorithm for finding an optimum weight perfect matching in a graph is described. It differs f... more An algorithm for finding an optimum weight perfect matching in a graph is described. It differs from Edmonds’ “blossom” algorithm in that a perfect matching is at hand throughout the algorithm, and a feasible solution to the dual problem is obtained only at termination. In many other respects, including its efficiency, it is similar to the blossom algorithm. Some advantages of this “primal” algorithm for certain post-optimality problems are described. The algorithm is used to prove that, if the weights are integers, then the dual problem has an optimal solution which is integer-valued. Finally, some graph-theoretic results on perfect matchings are derived.

Research paper thumbnail of On theorems of berge and fournier

Research paper thumbnail of On submodular function minimization

Research paper thumbnail of An algorithm for packing non-zero A-paths in group-labelled graphs

Research paper thumbnail of The optimal path-matching problem

Research paper thumbnail of Principally Unimodular Skew-Symmetric Matrices

Research paper thumbnail of Delta-Matroids, Jump Systems, Bisubmodular Polyhedra

Siam Journal on Discrete Mathematics, 1995

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