AWhat changed
Goemans and Williamson combine a semidefinite vector relaxation with random hyperplane rounding to obtain an expected approximately 0.87856 approximation for nonnegative weighted MAXCUT, with an epsilon loss for finite-precision optimization.
Scientific scope
Goemans and Williamson combine a semidefinite vector relaxation with random hyperplane rounding to obtain an expected approximately 0.87856 approximation for nonnegative weighted MAXCUT, with an epsilon loss for finite-precision optimization. The approximation guarantee concerns the stated weighted Max-Cut model, semidefinite relaxation and randomized hyperplane rounding. It is an expected approximation ratio under the model, not exact optimization or a deterministic guarantee for every single random cut. Solving the relaxation to the required precision has a cost. Extensions and later optimality/hardness results are separate.
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
- Michel X. Goemans · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- David P. Williamson · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Goemans and Williamson 1995: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
- Karger, Motwani and Sudan: Approximate Graph Coloring by Semidefinite Programming
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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