A new polynomial-time algorithm for linear programming

@article{Karmarkar1984ANP,
  title={A new polynomial-time algorithm for linear programming},
  author={N. Karmarkar},
  journal={Combinatorica},
  year={1984},
  volume={4},
  pages={373-395}
}
  • N. Karmarkar
  • Published 1984
  • Mathematics, Computer Science
  • Combinatorica
We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requiresO(n3.5L) arithmetic operations onO(L) bit numbers, wheren is the number of variables andL is the number of bits in the input. The running-time of this algorithm is better than the ellipsoid algorithm by a factor ofO(n2.5). We prove that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following… Expand
3,582 Citations
A very simple polynomial-time algorithm for linear programming
  • 1
  • PDF
A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs
  • É. Tardos
  • Mathematics, Computer Science
  • Oper. Res.
  • 1986
  • 456
Polynomial algorithms for linear programming over the algebraic numbers
  • 20
  • PDF
New geometric techniques for linear programming and graph partitioning
  • PDF
A primal-dual interior point method whose running time depends only on the constraint matrix
  • 135
On the Space Complexity of Linear Programming with Preprocessing
  • Y. Kalai, R. Raz
  • Computer Science, Mathematics
  • Electron. Colloquium Comput. Complex.
  • 2014
  • 9
  • PDF
Polynomial algorithms for LP over a subring of the algebraic integers with applications to LP with circulant matrices
  • 3
...
1
2
3
4
5
...

References

SHOWING 1-5 OF 5 REFERENCES
HOW GOOD IS THE SIMPLEX ALGORITHM
  • 975
Linear Programming and Extensions
  • 2,609
Introduction to Geometry
  • 799
Polynomial algorithms in linear programming
  • 1,627