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Tomonari Kitahara and Noriyoshi Sukegawa, A simple projection algorithm for linear programming problems, *Algorithmica*, 10.1007/s00453-018-0436-3, 2018.03, Fujishige et al. propose the LP-Newton method, a new algorithm for linear programming problem (LP). They address LPs which have a lower and an upper bound for each variable, and reformulate the problem by introducing a related zonotope. The LP-Newton method repeats projections onto the zonotope by Wolfe’s algorithm. For the LP-Newton method, Fujishige et al. show that the algorithm terminates in a finite number of iterations. Furthermore, they show that if all the inputs are rational numbers, then the number of projections is bounded by a polynomial in L, where L is the input length of the problem. In this paper, we propose a modification to their algorithm using a binary search. In addition to its finiteness, if all the inputs are rational numbers and the optimal value is an integer, then the number of projections is bounded by L+1, that is, a linear bound.. |

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Tomonari Kitahara, Shinji Mizuno, and Jianming Shi, The LP-Newton method for standard form linear programming problems, *Operations Research Letters*, 41, 426-429, 2013.09. |

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Tomonari Kitahara and Takashi Tsuchiya, A simple variant of the Mizuno-Todd-Ye predictor-corrector algorithm and its objective-function-free complexity, *SIAM Journal on Optimization*, 23, 1890-1903, 2013.09. |

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Tomonari Kitahara and Shinji Mizuno, A bound for the number of basic solutions generated by the simplex method, *Mathematical Programming*, 137, 579-586, 2013.02. |

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Tomonari Kitahara and Shinji Mizuno, On the number of solutions generated by the dual simplex method, *Operations Research Letters*, 40, 172-174, 2012.05. |