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Integer Programming with a Fixed Number of Variables
Abstract
It is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable. The proof depends on methods from geometry of numbers.
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Citations
Cited by
On Lovász’ lattice reduction and the nearest lattice point problem
Babai, L. (1986) · Combinatorica · doi:10.1007/bf02579403 · Cited by 938
PARAMETERIZED COMPLEXITY THEORY
Niedermeier, R. (2006) · Invitation to Fixed-Parameter Algorithms · doi:10.1093/acprof:oso/9780198566076.003.0013 · Cited by 574
Random walks in a convex body and an improved volume algorithm
Lovász, L., & Simonovits, M. (1993) · Random Structures & Algorithms · doi:10.1002/rsa.3240040402 · Cited by 409
Quantum algorithms for algebraic problems
Childs, A. M., & van Dam, W. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1 · Cited by 344
Bin Packing Approximation Algorithms: Survey and Classification
Coffman, E. G., Csirik, J., Galambos, G., Martello, S., & Vigo, D. (2013) · Handbook of Combinatorial Optimization · doi:10.1007/978-1-4419-7997-1_35 · Cited by 289
Metadata
- Authors
- Lenstra, H. W.
- Venue
- Mathematics of Operations Research
- Published
- 1983-11
- Volume
- 8
- Issue
- 4
- Pages
- 538-548
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2114616381
- Cited by
- 1,440
- References
- 0
- FWCI
- 15.70
- Type
- journal article
- Language
- en
- Open access
- closed
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How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
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- CoChat. (2026). Citation check: Integer Programming with a Fixed Number of Variables. https://app.cochat.ai/papers/10.1287/moor.8.4.538
- The paper
- Lenstra, H. W. (1983). Integer Programming with a Fixed Number of Variables. Mathematics of Operations Research. https://doi.org/10.1287/moor.8.4.538
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
