当图遍历遇到结构化偏好：统一框架与复杂性结果
When Graph Traversal Meets Structured Preferences: Unified Framework and Complexity Results
AI总结：
研究将偏好限制与经典图搜索范式相联系的框架，以图顶点为候选对象，用图搜索解释选民偏好排序。聚焦六种范式，探讨给定偏好配置文件在结构限制下是否有图支持的问题，给出NP难结果及部分多项式可解情况。
摘要：
偏好限制在计算社会选择中起重要作用。本文研究连接偏好限制与经典图搜索范式的框架。将候选者建模为图的顶点，把每个选民的偏好排序解释为根据图搜索遍历图的结果。聚焦六种基本范式，研究给定偏好配置文件在结构限制下是否允许图支持的问题。对于所有考虑的范式，当图支持最多有k条边时，该问题是NP难的，还将这些硬度结果扩展到图支持具有最大度k的情况。对于DFS，证明识别偏好配置文件是否允许树支持可以在多项式时间内解决。此外，现有结果意味着除BFS和LexBFS外，所有其余图遍历问题的多项式时间可解性，其复杂性仍然未知。
英文摘要：
Preference restrictions have played a significant role in computational social choice. This paper studies a framework that connects preference restrictions with classical graph search paradigms. We model candidates as vertices of a graph and interpret the preference ordering of each voter as the outcome of traversing the graph according to a graph search. We focus on six fundamental paradigms: breadth-first search (BFS), depth-first search (DFS), breadth-first search (LexBFS), lexicographic depth-first (LexDFS), maximum cardinality search (MCS), and maximal neighborhood search (MNS). Within this framework, we study the problem of determining whether a given preference profile admits a graph support subject to structural restrictions, that is, whether there exists a graph such that each preference ordering can be generated by traversing the graph under the chosen paradigm. For all considered paradigms, we show that this problem is NP-hard when the graph support is required to have at most $k$ edges, where $k$ is a given integer. We further extend these hardness results to the case where the graph support is required to have maximum degree $k$. For DFS, we prove that recognizing whether a preference profile admits a tree support can be solved in polynomial time. Moreover, existing results imply polynomial-time solvability of the problem for all remaining graph traversals, except BFS and LexBFS, for which the complexity remains open.
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