Abstract
This work develops a two-dimensional cellular automaton (CA) which solves single source shortest path problem for a grid graph. Grid graphs are represented as configurations of the CA, and maximum degree of a node is considered as four. Nodes and edges of the graph are modeled by cells with different state sets. The cells for nodes use a rule to update their states whereas the rest cells including the cells for edges use another rule. That is, two rules are used by the automaton which makes it a non-uniform CA. The worst case time complexity for the scheme is \(\mathcal {O}(n)\) where n is the total number of nodes in the connected graph.
This work is supported by the SERB, Govt. of India sponsored project titled “Computational Problems and Cellular Automata” (File No: EMR/2017/001571).
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References
Roy, S., Ray, A., Das, S.: A cellular automaton that solves distributed spanning tree problem. J. Comput. Sci. 26, 39–54 (2018)
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Barman, D., Das, S. (2021). A Cellular Automaton that Computes Shortest Paths in Grid Graph. In: Gwizdałła, T.M., Manzoni, L., Sirakoulis, G.C., Bandini, S., Podlaski, K. (eds) Cellular Automata. ACRI 2020. Lecture Notes in Computer Science(), vol 12599. Springer, Cham. https://doi.org/10.1007/978-3-030-69480-7_1
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DOI: https://doi.org/10.1007/978-3-030-69480-7_1
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