We present a variant of the Simplex method which requires on the average at most 2(min(m,d)+1)-squared pivots to solve the linear program min cTx, Ax>=b, x>=0 with (A(epsilon)R)mxd. The underlying probabilistic distribution is assumed to be invariant under inverting the sense of any subset of the inequalities. In particular, this implies that under Smale's spherically symmetric model this variant requires an average of no more than 2(d+1)-squared pivots, independent of m, where d<=m.
Title
A Simplex Variant Solving An m x d Linear Program in O(min(m squared, d squared)) Expected Number of Pivot Steps
Published
1983-12-01
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
CSD-83-158
Type
Text
Extent
19 p
Archive
The Engineering Library
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