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Ants are known to be able to find paths of minimal length between the nestand food sources. The deposit of pheromones while they search for food andtheir chemotactical response to them has been proposed as a crucial element inthe mechanism for finding minimal paths. We investigate both individual andcollective behavior of ants in some simple networks representing basic mazes.The character of the graphs considered is such that it allows a fully rigorousmathematical treatment via analysis of some markovian processes in terms ofwhich the evolution can be represented. Our analytical and computationalresults show that in order for the ants to follow shortest paths between nestand food, it is necessary to superimpose to the ants' random walk thechemotactic reinforcement. It is also needed a certain degree of persistence sothat ants tend to move preferably without changing their direction much. It isalso important the number of ants, since we will show that the speed forfinding minimal paths increases very fast with it.

Ant foraging and minimal paths in simple graphs