A Proof by the Simplex Method for the Diameter of a (0,1)-Polytope
نویسندگان
چکیده
Naddef [3] shows that the Hirsch conjecture is true for (0,1)-polytopes by proving that the diameter of any (0, 1)-polytope in d-dimensional Euclidean space is at most d. In this short paper, we give a simple proof for the diameter. The proof is based on the number of solutions generated by the simplex method for a linear programming problem. Our work is motivated by Kitahara and Mizuno [2], in which they get upper bounds for the number of different solutions generated by the simplex method.
منابع مشابه
The Simplex Method and 0-1 Polytopes
We will derive two results of the primal simplex method by constructing simple LP instances on 0-1 polytopes. First, for any 0-1 polytope and any of its two vertices, we can construct an LP instance for which the simplex method finds a path between them, whose length is at most the dimension of the polytope. This proves a well-known result that the diameter of any 0-1 polytope is bounded by its...
متن کاملSimplex-type algorithm for optimizing a pseudolinear quadratic fractional function over a polytope
Recently Cambini and Carosi described a characterization of pseudolinearity of quadratic fractional functions. A reformulation of their result was given by Rapcsák. Using this reformulation, in this paper we describe an alternative proof of the Cambini–Carosi Theorem. Our proof is shorter than the proof given by Cambini–Carosi and less involved than the proof given by Rapcsák. As an application...
متن کاملThe k-assignment polytope
In this paper we study the structure of the k-assignment polytope, whose vertices are the m× n (0,1)-matrices with exactly k 1:s and at most one 1 in each row and each column. This is a natural generalisation of the Birkhoff polytope and many of the known properties of the Birkhoff polytope are generalised. A representation of the faces by certain bipartite graphs is given. This tool is used to...
متن کاملA Randomized Polynomial-Time Simplex Algorithm for Linear Programming (Preliminary Version)
We present the first randomized polynomial-time simplex algorithm for linear programming. Like the other known polynomial-time algorithms for linear programming, its running time depends polynomially on the number of bits used to represent its input. We begin by reducing the input linear program to a special form in which we merely need to certify boundedness. As boundedness does not depend upo...
متن کاملDevelopment of RMPC Algorithm for Compensation of Uncertain Time-Delay and Disturbance in NCS
In this paper, a synthesis method based on robust model predictive control is developed for compensation of uncertain time-delays in networked control systems with bounded disturbance. The proposed method uses linear matrix inequalities and uncertainty polytope to model uncertain time-delays and system disturbances. The continuous system with time-delay is discretized using uncertainty po...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011