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：我们针对近邻旅行商问题（CETSP）提出了一种快速、拟线性时间复杂度的启发式算法。CETSP是欧几里得TSP的连续泛化形式，其中每个目标均为需被路径穿过的圆盘。该方法将配对中心聚类范式扩展至圆形邻域：在层次聚类阶段，利用R*-树高效执行空间查询，将邻近圆盘合并为代理圆；在构造阶段，逐步扩展层次结构形成可行路径，同时维护并局部优化路径点。通过轻量级局部改进（选择性重插入与约束点重优化），在保证可扩展性的前提下减少局部低效性。该算法在期望O(n log n)时间内运行，针对Mennell数据集中重构的基准实例，其求解质量与当前最优解偏差约为0-2%，而运行时间比基于种群的元启发式算法低数个数量级。该方法以牺牲部分最终解最优性为代价，显著提升求解速度与可扩展性，适用于超大规模CETSP实例。