Cellular Automata Applications in Shortest Path Problem

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 201

Cellular automaton model of crowd evacuation inspired by slime mould

In all the living organisms, the self-preservation behaviour is almost universal. Even the most simple of living organisms, like slime mould, is typically under intense selective pressure to evolve a response to ensure their evolution and safety in the best possible way. On the other hand, evacuation of a place can be easily characterized as one of the most stressful situations for the individuals taking part on it. Taking inspiration from the slime mould behaviour, we are introducing a computational bio-inspired model crowd evacuation model. Cellular Automata (CA) were selected as a fully parallel advanced computation tool able to mimic the Physarum’s behaviour. In particular, the proposed CA model takes into account while mimicking the Physarum foraging process, the food diffusion, the organism’s growth, the creation of tubes for each organism, the selection of optimum tube for each human in correspondence to the crowd evacuation under study and finally, the movement of all humans at each time step towards near exit. To test the model’s efficiency and robustness, several simulation scenarios were proposed both in virtual and real-life indoor environments (namely, the first floor of office building B of the Department of Electrical and Computer Engineering of Democritus University of Thrace). The proposed model is further evaluated in a purely quantitative way by comparing the simulation results with the corresponding ones from the bibliography taken by real data. The examined fundamental diagrams of velocity–density and flow–density are found in full agreement with many of the already published corresponding results proving the adequacy, the fitness and the resulting dynamics of the model. Finally, several real Physarum experiments were conducted in an archetype of the aforementioned real-life environment proving at last that the proposed model succeeded in reproducing sufficiently the Physarum’s recorded behaviour derived from observation of the aforementioned biological laboratory experiments