一种针对具有无增益 Leontief 替代系统的线性规划问题的组合式认证算法
A Combinatorial Certifying Algorithm for Linear Programming Problems with Gainfree Leontief Substitution Systems
AI总结：
本文针对无增益 Leontief 替代系统的线性规划问题，提出首个组合式且强多项式时间的认证算法，并据此证明一类 Horn 系统可行性问题也存在组合认证算法。
摘要：
具有无增益 Leontief 替代系统的线性规划（LP）问题已在经济学和运筹学中得到深入研究，其中包括一类 Horn 系统的可行性问题，这类问题出现在多面体组合学和逻辑学等领域。该 LP 问题子类存在强多项式时间算法，而为一般 LP 问题设计这样的算法是数学优化与计算机科学中重大的理论开放问题之一。近来，软件工程领域对设计认证算法给予了大量关注，因为这些算法使人们能够通过简单计算确认程序输出的正确性。本文中，我们针对具有无增益 Leontief 替代系统的 LP 问题，给出首个组合式（且为强多项式时间）认证算法。作为附带成果，我们肯定地回答了一个开放问题，即该类 Horn 系统的可行性问题是否存在组合式认证算法。
英文摘要：
Linear programming (LP) problems with gainfree Leontief substitution systems have been intensively studied in economics and operations research, and include the feasibility problem of a class of Horn systems, which arises in, e.g., polyhedral combinatorics and logic. This subclass of LP problems admits a strongly polynomial time algorithm, where devising such an algorithm for general LP problems is one of the major theoretical open questions in mathematical optimization and computer science. Recently, much attention has been paid to devising certifying algorithms in software engineering, since those algorithms enable one to confirm the correctness of outputs of programs with simple computations. In this paper, we provide the first combinatorial (and strongly polynomial time) certifying algorithm for LP problems with gainfree Leontief substitution systems. As a by-product, we answer affirmatively an open question whether the feasibility problem of the class of Horn systems admits a combinatorial certifying algorithm.
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