属于图中每个最小支配集的顶点及其与交通共享系统的联系——以坎波德直布罗陀地区为研究案例
Vertices that belong to every minimum dominating set of a graph and their connection with transportation sharing systems with study cases in Campo de Gibraltar area
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中文总结 AI 辅助
本研究提出图支配强制顶点理论，证明其识别为co-NP难，给出数量上界，并用迭代贪婪算法在西班牙两城市定位滑板车共享站点。
中文摘要 AI 辅助
本研究通过应用图顶点支配设定，解决共享交通系统（如微出行网络）设计中的公平性和可达性挑战的理论模型。工作重点在于识别支配强制顶点，即属于图中最小基数支配集的节点，这些节点对应于维持系统效率和覆盖范围所必需的关键、不可协商的站点位置。从理论角度看，本文首先证明了确定给定顶点是否为支配强制顶点是co-NP难的，确立了在大规模网络中精确识别的计算不可行性。为了分析图结构，建立了支配强制顶点最大数量的尖锐理论界限，证明其数量上限为图阶数的三分之一，并为达到此界限的图提供了完整的结构刻画，同时给出了无支配强制顶点的树的刻画。为克服实际城市环境中的计算限制，研究采用迭代贪婪元启发式框架生成最小支配集，并根据节点在迭代中的出现频率近似关键强制节点。该方法在强网格图上得到验证，并应用于西班牙坎波德直布罗陀地区阿尔赫西拉斯和拉利内亚德拉孔塞普西翁两个城市的真实道路网络模型，成功确定了两个城市中滑板车共享站点的候选位置。
英文摘要
This study addresses a theoretical model regarding equity and accessibility challenges in designing shared transportation systems (such as micro-mobility networks) by applying graph-vertex domination setting. The work focuses on identifying dominating forced vertices, that represent nodes belonging to every dominating set of a graph of the smallest possible cardinality, and which correspond to critical, non-negotiable station locations essential for maintaining system efficiency and coverage. From a theoretical perspective, in the paper it is first demonstrated that determining whether a given vertex is a dominating forced vertex is co-NP-hard, establishing the computational infeasibility of exact identification in large networks. To analyze graph structures, sharp theoretical bounds on the maximum number of dominating forced vertices are established, proving that their count is bounded above by one-third of the order of the graph, and provide complete structural characterizations for graphs achieving this bound, as well as, trees with no dominating forced vertices. To overcome computational limits in practical urban settings, the study uses an iterated greedy metaheuristic framework to generate minimal dominating sets and approximate critical forced nodes based on their appearance frequency across iterations. The methodology is validated on strong grid graphs and applied to real-world road network models of Algeciras and La Línea de la Concepción, two cities in the area of Campo de Gibraltar, Spain, which successfully pinpoints candidate location points for scooter-sharing stations across both cities.
发表机构
- UCA（加的斯大学）
机构由 AI 辅助整理，请以论文原文为准。
