# Improved algorithms for integer programming and related lattice problems

@inproceedings{Kannan1983ImprovedAF, title={Improved algorithms for integer programming and related lattice problems}, author={R. Kannan}, booktitle={STOC '83}, year={1983} }

The integer programming problem is: Given m×n and m×l matrices A and b respectively of integers, find whether, there exists an all integer n×l vector x satisfying the m inequalities A×≤b. In settling an important open problem, Lenstra (1981) showed in an elegant way that when n, the number of dimensions is fixed, there is a polynomial-time algorithm to solve this problem. His algorithm achieves a running-time of 0(cn3•p(length of data)) where p is some polynomial and c a constant independent of… Expand

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#### References

SHOWING 1-2 OF 2 REFERENCES

The computational complexity of simultaneous Diophantine approximation problems

- Computer Science, Mathematics
- 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)
- 1982

151 Highly Influential

The computational complexity of simultaneous Diophantine approximation problems

- Mathematics
- FOCS 1982
- 1982

20 Highly Influential