保留双向性的反馈弧集问题及其在教师招聘网络分析中的应用
The Bidirectionality-Preserving Feedback Arc Set Problem with an Application to Faculty Hiring Network Analysis
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中文总结 AI 辅助
本研究提出含双向弧有向图的保留双向性反馈弧集问题，扩展了Slater规则，引入二元规划公式与多项式时间算法，并将其应用于IEOR系教师招聘网络的声望分析。
中文摘要 AI 辅助
本研究提出一种新的组合优化问题，用于揭示含双向弧有向图所蕴含的严格与非严格层级结构。研究表明该问题包含经典的反馈弧集问题作为特例，其解扩展了名为Slater规则的锦标赛解。我们引入并比较两种二元规划公式，还提出一种多项式时间搜索算法，用于从其解中获取有序层级。该方法被应用于教师招聘网络问题，使用Del Castillo等人（2020）先前收集的数据集，通过教师招聘交易来刻画工业/系统/运筹学（IEOR）系的声望/等级。
英文摘要
This work introduces a novel combinatorial optimization problem to uncover strict and non-strict hierarchical structures underlying digraphs with bidirected arcs. We show that the problem includes the seminal feedback arc set problem as a special case, and that its solution extends a tournament solution known as Slater's rule. We introduce and compare two binary programming formulations and also introduce a polynomial-time search algorithm for obtaining an ordered hierarchy from their solution. The methodology is applied to the faculty hiring network problem using a dataset previously collected by Del Castillo et al. (2020) to characterize the prestige/rank of Industrial/Systems/Operations Research (IEOR) departments using faculty hiring transactions.
