  We present an efficient and exact Monte Carlo algorithm to simulate
reversible aggregation of particles with dedicated binding sites. This method
introduces a novel data structure of dynamic bond tree to record clusters and
sequences of bond formations. The algorithm achieves a constant time cost for
processing cluster association and a cost between $\mathcal{O}(\log M)$ and
$\mathcal{O}(M)$ for processing bond dissociation in clusters with $M$ bonds.
The algorithm is statistically exact and can reproduce results obtained by the
standard method. We applied the method to simulate a trivalent ligand and a
bivalent receptor clustering system and obtained an average scaling of
$\mathcal{O}(M^{0.45})$ for processing bond dissociation in acyclic
aggregation, compared to a linear scaling with the cluster size in standard
methods. The algorithm also demands substantially less memory than the
conventional method.
