Circuit and Graver walks and linear and integer programming

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2024-10-01 DOI:10.1016/j.disopt.2024.100862

Shmuel Onn

引用次数: 0

Abstract

We show that a circuit walk from a given feasible point of a given linear program to an optimal point can be computed in polynomial time using only linear algebra operations and the solution of the single given linear program. We also show that a Graver walk from a given feasible point of a given integer program to an optimal point is polynomial time computable using an integer programming oracle, but without such an oracle, it is hard to compute such a walk even if an optimal solution to the given program is given as well. Combining our oracle algorithm with recent results on sparse integer programming, we also show that Graver walks from any point are polynomial time computable over matrices of bounded tree-depth and subdeterminants.

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电路和格拉夫行走以及线性和整数编程

我们证明，只需使用线性代数运算和单个给定线性规划的解，就能在多项式时间内计算从给定线性规划的给定可行点到最优点的电路行走。我们还证明，从给定整数程序的给定可行点到最优点的 Graver 走法可以用整数编程神谕在多项式时间内计算，但如果没有这样的神谕，即使给定程序的最优解也很难计算这样的走法。结合我们的神谕算法和稀疏整数编程的最新成果，我们还证明了在有界树深度和子决定子矩阵上，从任意点出发的格拉夫行走都是多项式时间可计算的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.