A simplex variant solving an m × d linear program in O(min(m2, d2) expected number of pivot steps

Ilan Adler, Richard M. Karp, Ron Shamir

Research output: Contribution to journalArticlepeer-review

Abstract

We present a variant of the Simplex method which requires on the average at most 2 (min(m, d) + 1)2 pivots to solve the linear program min cT, Ax ≥ b, x ≥ 0 with A ε Rm×d. 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)2 pivots, independent of m, where d ≤ m.

Original languageEnglish
Pages (from-to)372-387
Number of pages16
JournalJournal of Complexity
Volume3
Issue number4
DOIs
StatePublished - Dec 1987

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