TY - JOUR
T1 - A simplex variant solving an m × d linear program in O(min(m2, d2) expected number of pivot steps
AU - Adler, Ilan
AU - Karp, Richard M.
AU - Shamir, Ron
PY - 1987/12
Y1 - 1987/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0003490380&partnerID=8YFLogxK
U2 - 10.1016/0885-064X(87)90007-0
DO - 10.1016/0885-064X(87)90007-0
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AN - SCOPUS:0003490380
VL - 3
SP - 372
EP - 387
JO - Journal of Complexity
JF - Journal of Complexity
SN - 0885-064X
IS - 4
ER -