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Finding the shortest path in a graph has applications to a wide range ofoptimization problems. However, algorithmic methods scale with the size of thegraph in terms of time and energy. We propose a method to solve the shortestpath problem using circuits of nanodevices called memristors and validate it ongraphs of different sizes and topologies. It is both valid for anexperimentally derived memristor model and robust to device variability. Thetime and energy of the computation scale with the length of the shortest pathrather than with the size of the graph, making this method particularlyattractive for solving large graphs with small path lengths.

A scalable method to find the shortest path in a graph with circuits of memristors