AWhat changed
Lenstra showed that integer linear feasibility can be solved in polynomial input-length time when the number of integer variables is fixed, using lattice geometry and reduction to lower-dimensional problems.
Scientific scope
Lenstra showed that integer linear feasibility can be solved in polynomial input-length time when the number of integer variables is fixed, using lattice geometry and reduction to lower-dimensional problems. The polynomial-time result fixes the number of integer variables. Its dimension-dependent cost is not a polynomial bound uniform in arbitrary dimension. Rational input encoding and geometric subroutines matter. Mixed variants have their own assumptions. The theorem is not evidence that every integer program is easy in practice.
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
- H. W. Lenstra Jr. · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Lenstra, Integer Programming with a Fixed Number of Variables, MOR 8(4)538-548(1983), author-hosted journal copy
- Publisher Crossref deposit for 10.1287/moor.8.4.538
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