A group of people searches for a lost item in a large park. Some get tired and leave, others join along the way. The number of searchers is constantly changing. How does this affect the search time? Until now, science had no clear answer.
In a new study, a general model of such a process has been built. In it, independent participants randomly enter and leave the search. This was called dynamic redundancy and mortality. It turned out that even with minimal assumptions about the searchers' movement itself, one can accurately calculate the average time to reach the target.
The model was tested on a simple case: one-dimensional random walk. If a searcher can only move left or right along a line, then the changing team composition sometimes speeds up the search and sometimes slows it down: it all depends on how often participants arrive and leave.
The practical benefit is obvious. From animals foraging to distributed computing, the number of active agents fluctuates everywhere. The new theory provides a tool for calculating optimal strategies under such conditions.
In some regimes, a fluctuating team finds the target faster than a constant group of the same average size.