The reused supergroup index does not require additional communication, because of an implementation detail in the annihilation step. All walkers on the same determinant are collected to the same process, to facilitate the annihilation of newly spawned walkers from different parent determinants. This implies that in the subsequent spawning step all walkers belonging to a given determinant will reside on one process. Every walker that attempts to spawn from this determinant can look up the index without any communication across processes.