标题： 复杂网络的分数维和重正化避核碰撞及叶节点选项算法 显示英文标题

标题： Hub-collision avoidance and leaf-node options algorithm for fractal dimension and renormalization of complex networks

摘要： 盒覆盖方法在复杂网络的分数维性质识别和重整化分析中起着根本性的作用。本研究提出了枢纽碰撞规避和叶节点选择（HALO）算法。在盒子采样的过程中，确定了前向采样规则（用于避免枢纽碰撞）和后向采样规则（用于优先选择叶节点），以实现双向网络遍历，从而减少采样的随机性。在盒子选择的过程中，通过不断移除小盒子来优先选择较大的必要盒子加入解中。实验中将紧致盒子燃烧（CBB）算法、最大排除质量燃烧（MEMB）算法、重叠盒子覆盖（OBCA）算法以及结合小盒子去除策略与最大盒子采样且采样密度为30（SM30）的算法与HALO进行了比较。九个真实网络的结果表明，HALO达到了最高的性能评分，并分别比对比算法少用了11.40%、7.67%、2.18%和8.19%的盒子。算法的确定性显著提高，覆盖四个标准网络估算的分数维更加准确。此外，不同于MEMB或OBCA，HALO不受枢纽紧密度的影响，在不同网络中表现出稳定性能。最后，HALO与其他对比算法的时间复杂度均为O(N^2)，这是合理且可接受的。 显示英文摘要

摘要： The box-covering method plays a fundamental role in the fractal property recognition and renormalization analysis of complex networks. This study proposes the hub-collision avoidance and leaf-node options (HALO) algorithm. In the box sampling process, a forward sampling rule (for avoiding hub collisions) and a reverse sampling rule (for preferentially selecting leaf nodes) are determined for bidirectional network traversal to reduce the randomness of sampling. In the box selection process, the larger necessary boxes are preferentially selected to join the solution by continuously removing small boxes. The compact-box-burning (CBB) algorithm, the maximum-excluded-mass-burning (MEMB) algorithm, the overlapping-box-covering (OBCA) algorithm, and the algorithm for combining small-box-removal strategy and maximum box sampling with a sampling density of 30 (SM30) are compared with HALO in experiments. Results on nine real networks show that HALO achieves the highest performance score and obtains 11.40%, 7.67%, 2.18%, and 8.19% fewer boxes than the compared algorithms, respectively. The algorithm determinism is significantly improved. The fractal dimensions estimated by covering four standard networks are more accurate. Moreover, different from MEMB or OBCA, HALO is not affected by the tightness of the hubs and exhibits a stable performance in different networks. Finally, the time complexities of HALO and the compared algorithms are all O(N^2), which is reasonable and acceptable.