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Pheromones are a chemical substance produced and released by ants as means ofcommunication. In this work we present the minimum amount of pheromonesnecessary and sufficient for a colony of ants (identical mobile agents) todeterministically find a food source (treasure), assuming that each ant has thecomputational capabilities of either a Finite State Machine (FSM) or a TuringMachine (TM). In addition, we provide pheromone-based foraging algorithmscapable of handling fail-stop faults.  In more detail, we consider the case where $k$ identical ants, initiallylocated at the center (nest) of an infinite two-dimensional grid andcommunicate only through pheromones, perform a collaborative search for anadversarially hidden treasure placed at an unknown distance $D$. We begin byproving a tight lower bound of $\Omega(D)$ on the amount of pheromones requiredby any number of FSM based ants to complete the search, and continue to reducethe lower bound to $\Omega(k)$ for the stronger ants modeled as TM. We providealgorithms which match the aforementioned lower bounds, and still terminate inoptimal $\mathcal{O}(D + D^2 / k)$ time, under both the synchronous andasynchronous models. Furthermore, we consider a more realistic setting, wherean unknown number $f < k$ of ants may fail-stop at any time; we providefault-tolerant FSM algorithms (synchronous and asynchronous), that terminate in$\mathcal{O}(D + D^2/(k-f) + Df)$ rounds and emit no more than the sameasymptotic minimum number of $\mathcal{O}(D)$ pheromones overall.

Optimal and Resilient Pheromone Utilization in Ant Foraging