We introduce a fast, quasi-linear-time heuristic for the Close-Enough Traveling Salesman Problem (CETSP), a continuous generalization of the Euclidean TSP in which each target is a disk that must be intersected. The method adapts the pair-center clustering paradigm to circular neighborhoods: a hierarchical clustering phase merges nearby disks into proxy circles using an R*-tree for efficient spatial queries, and a construction phase incrementally expands the hierarchy into a feasible tour while maintaining and locally optimizing tour points. Lightweight local improvements, selective reinsertion and constrained point reoptimization, reduce local inefficiencies without compromising scalability. The algorithm runs in expected O(n log n) time and, on benchmark instances reconstructed from the Mennell dataset, produces solutions within roughly 0-2% of state-of-the-art best-known values while requiring orders-of-magnitude less runtime than population-based metaheuristics. The approach trades some final-solution optimality for dramatic gains in speed and scalability, making it suitable for very large CETSP instances.

翻译：我们提出了一种用于“充分临近旅行商问题”（CETSP）的快速准线性时间启发式算法，该问题是欧几里得旅行商问题（TSP）的连续推广，其中每个目标是一个必须被穿过的圆盘。该方法将配对中心聚类范式适配到圆形邻域：分层聚类阶段利用R*-树进行高效空间查询，将邻近圆盘合并为代理圆；构建阶段逐步将分层结构扩展为可行路径，同时维护并局部优化路径点。轻量级局部改进（选择性重插入与约束点重优化）在不牺牲可扩展性的前提下减少了局部低效性。该算法以期望O(n log n)时间运行，在从Mennell数据集重构的基准实例上，其解与最新已知最优值的偏差约为0-2%，而所需运行时间比基于种群的元启发式算法少几个数量级。该方法以牺牲部分最终解最优性为代价，换取了速度与可扩展性的显著提升，使其适用于大规模CETSP实例。