Edmonds and Karp: shortest augmenting paths, cost potentials and scaling for network flows

What changed

Edmonds and Karp bounded shortest-path flow augmentations independently of capacity precision, used nonnegative reduced costs for minimum-cost flow, and developed capacity scaling with repair of lost optimality.

Scientific scope

Edmonds and Karp bounded shortest-path flow augmentations independently of capacity precision, used nonnegative reduced costs for minimum-cost flow, and developed capacity scaling with repair of lost optimality. The original algorithms concern finite flow networks with stated capacities/costs and arithmetic accounting. Shortest augmenting paths, potential updates and scaling variants have separate assumptions and bounds. They are not a universal strongly polynomial guarantee for every later min-cost-flow formulation, nor an independently measured implementation speedup. Later refinements retain separate credit.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• Jack Edmonds · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• Richard M. Karp · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Edmonds and Karp, Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems (1972) — complete original scan

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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