On the ability of Swarms to compute the 3-coloring of graphs

Swarm Intelligent Systems are computational models of the spatial evolution of populations explaining it as a global behavior emerging from locally controlled movements, which are guided by decisions taken on the basis of local information. The increase of agents’ cognitive capabilities, endowing them with memory and with the ability of selecting the rules of movement depending on an internal state allows the application of Self-Organizing Particle Systems (SOPS) to heuristic problem solving. Our focus in this work is on the complex emergent behavior arising when endowing the individuals with another elementary cognitive ability: the perception of the affinity of another individual. Each individual agent perceives other individual agents as friends or enemies. The first class is attractive while the second is repulsive. Metaphorically, the first class is associated with amity, security and comfort while the second is associated with danger, enemies and things to avoid. This local individual perception produces the emergence of teams and classes at a global level. This behavior produces an spatial distribution that can be interpreted under the appropriate metaphor as solving a particular computational problem. Applying this metaphor, we have found empirically that Self-Organizing Particle Systems can be designed to perform the task of 3-coloring graphs with the same precision as the Brélaz coloring heuristic, which is the best greedy heuristic known for this purpose.