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Published in:
01-06-2014 | Erratum
Erratum to: Discussions on Hirsch Conjecture and Existence of Strongly Polynomial-time Simplex Variants
Published in: Annals of Data Science | Issue 2/2014
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Excerpt
In the original published version of this article, several errors are unfortunately found. The illustrations and corrections of these errors are listed as below:
1.
Title Discussions on Hirsch Conjecture and The Existence of Strongly Polynomial: Time Simplex Variants Correction: Discussions on Hirsch Conjecture and Existence of Strongly Polynomial-time Simplex Variants
2.
The row of Example 4.1 in page 59: Example 4.1. Given \(^{0}{\varvec{g}} = -{\varvec{b}}^{T}=(-4,-1,-4,-6,-2),\; F_{0}=(7,4,7,6,5)\!\in \) Correction: Example 4.1. Given \(^{0}{\varvec{g}}=-{\varvec{b}}^{T}=(-4,-1,-4,-6,-2), F_{0}=(7,4,7,9,5)\!\in \)
3.
The rows from second row to fifth row, under the tableau in page 66: \(k=0\). \(\varDelta =\varnothing \), there is no door at \(F_{0}=(7,4,7,6,5)\), go to Step 3, Step 3 Getting next stage point and the door cone \(C_{1}\):
Correction: \(k=0. \varDelta =\varnothing \), there is no door at \(F_{0}=(7,4,7,9,5)\), go to Step 3, Step 3 Getting next stage point and the door cone \(C_{1}\):
$$\begin{aligned} F_{1}&= F_{k+1}=NextStagePoint(F_{k},\underline{{\varvec{g}}}_{{\downarrow \ldots (k)}})\\&= NextStagePoint(F_{0},{}^{0}{\varvec{g}})=(3,3,3,3); \end{aligned}$$
$$\begin{aligned} F_{1}&= F_{k+1}=NextStagePoint(F_{k},\underline{{\varvec{g}}}_{{\downarrow \ldots (k)}})\\&= NextStagePoint(F_{0}, {}^{0}{\varvec{g}})=(3,3,3,3,3); \end{aligned}$$