ACM Computing Surveys (CSUR)
An all pairs shortest path algorithm with expected time O(n2logn)
SIAM Journal on Computing
A distributed shortest path algorithm for a planar network
Information and Computation
Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length
Journal of the ACM (JACM)
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Communications of the ACM
Fibonacci Heaps And Their Uses In Improved Network Optimization Algorithms
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Computing with solitons: a review and prospectus
Collision-based computing
Experimental Reaction–Diffusion Chemical Processors for Robot Path Planning
Journal of Intelligent and Robotic Systems
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Grand challenge 7: journeys in non-classical computation
VoCS'08 Proceedings of the 2008 international conference on Visions of Computer Science: BCS International Academic Conference
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In this paper, we show how to find the shortest path between given nodes of a mesh with weighted edges. We use a cellular automaton which exhibits autowave patterns, where a wave of auto-excitation originates in source node, spreads around the mesh, and modifies states of the cells to make a stationary pattern isomorphed to the shortest path from source node to destination one. For different formulations of the shortest path problem, and various cellular automata (which solve it), we proved the bounds of complexity. For the sake of clarity, we present several examples of cellular automata computation of the shortest path. They are illustrated in detail.