Linear programming in linear time when the dimension is fixed (1984)
| Venue: | J. ACM |
| Citations: | 168 - 13 self |
BibTeX
@ARTICLE{Megiddo84linearprogramming,
author = {Nimrod Megiddo},
title = {Linear programming in linear time when the dimension is fixed},
journal = {J. ACM},
year = {1984},
volume = {31},
pages = {114--127}
}
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Abstract
Abstract. It is demonstrated that the linear programming problem in d variables and n constraints can be solved in O(n) time when d is fixed. This bound follows from a multidimensional search technique which is applicable for quadratic programming as well. There is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n. Categories and Subject Descriptors: F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems-computations on matrices; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems-geometrical problems and computations; sort-ing and searching; G. 1.6 [Mathematics of Computing]: Optimization-linear programming
