McCormick, S. Thomas
Overview
Works:  4 works in 10 publications in 1 language and 15 library holdings 

Classifications:  QA76.952, 330 
Publication Timeline
.
Most widely held works by
S. Thomas McCormick
A faster capacity scaling algorithm for minimum cost submodular flow by
Lisa Fleischer(
Book
)
6 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
Abstract: "We describe an O(n⁴h min[log U, n² log n]) capacity scaling algorithm for the minimum cost submodular flow problem. Our algorithm modifies and extends the EdmondsKarp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem. The modification entails scaling a relaxation parameter [delta]. Capacities are relaxed by attaching a complete directed graph with uniform arc capacity [delta] in each scaling phase. We then modify a feasible submodular flow by relaxing the submodular constraints, so that complementary slackness is satisfied. This creates discrepancies between the boundary of the flow and the base polytope of a relaxed submodular function. To reduce these discrepancies, we use a variant of the successive shortest path algorithm that augments flow along min cost paths of residual capacity at least [delta]. The shortest augmenting path subroutine we use is a variant of Dijkstra's algorithm modified to handle exchange capacity arcs efficiently. The result is a weakly polynomial time algorithm whose running time is better than any existing submodular flow algorithm when U is small and C is big. We also show how to use max mean cuts to make the algorithm strongly polynomial. The resulting algorithm is the first capacity scaling algorithm to match the current best strongly polynomial bound for submodular flow."
6 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
Abstract: "We describe an O(n⁴h min[log U, n² log n]) capacity scaling algorithm for the minimum cost submodular flow problem. Our algorithm modifies and extends the EdmondsKarp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem. The modification entails scaling a relaxation parameter [delta]. Capacities are relaxed by attaching a complete directed graph with uniform arc capacity [delta] in each scaling phase. We then modify a feasible submodular flow by relaxing the submodular constraints, so that complementary slackness is satisfied. This creates discrepancies between the boundary of the flow and the base polytope of a relaxed submodular function. To reduce these discrepancies, we use a variant of the successive shortest path algorithm that augments flow along min cost paths of residual capacity at least [delta]. The shortest augmenting path subroutine we use is a variant of Dijkstra's algorithm modified to handle exchange capacity arcs efficiently. The result is a weakly polynomial time algorithm whose running time is better than any existing submodular flow algorithm when U is small and C is big. We also show how to use max mean cuts to make the algorithm strongly polynomial. The resulting algorithm is the first capacity scaling algorithm to match the current best strongly polynomial bound for submodular flow."
Polynomial methods for separable convex optimization in unimodular linear spaces with applications to circulations and cocirculations
in networks by
A. V Karzanov(
Book
)
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
Strongly polynomial bounds for multiobjective and parametric global minimum cuts in graphs and hypergraphs(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
A faster capacity scaling algorithm for minimum cost submodular flow(
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
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Alternative Names
Cormick, S. Thomas Mc
Mac Cormick, S. Thomas
MacCormick, S. T.
MacCormick, S. Thomas
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