  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.
