Goldberg–Tarjan: computing maximum flow with preflows and local push–relabel operations

What changed

Goldberg and Tarjan developed a maximum-flow method that temporarily permits excess flow at intermediate vertices, then uses local pushes and valid height labels to restore conservation and obtain a maximum feasible flow.

Scientific scope

Goldberg and Tarjan developed a maximum-flow method that temporarily permits excess flow at intermediate vertices, then uses local pushes and valid height labels to restore conservation and obtain a maximum feasible flow. The method maintains a preflow and admissible height labels on a finite capacitated network. Intermediate excess is permitted; termination and feasibility need the prescribed push/relabel conditions. Variant-specific arithmetic complexity bounds are not arbitrary-precision or real-world throughput measurements. Parallel and later optimized implementations require their own guarantees.

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

• Andrew V. Goldberg · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• Robert E. Tarjan · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• A. V. Goldberg and R. E. Tarjan, A New Approach to the Maximum-Flow Problem (1988) — complete journal article

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

Full scientific record · Browse contribution grades · Request a correction