Many big data have interconnected and dynamic graph structures growing over time. Analyzing these graphical data requires the hidden relationship between the nodes in the graphs to be identified, which has conventionally been achieved by finding the effective similarity. However, graphs are generally non-Euclidean, which does not allow finding it. In this study, the non-Euclidean graphs are mapped to a specific crossbar array (CBA) composed of self-rectifying memristors and metal cells at the diagonal positions. The sneak current, an intrinsic physical property in the CBA, allows for the identification of the similarity function. The sneak-current-based similarity function indicates the distance between the nodes, which can be used to predict the probability that unconnected nodes will be connected in the future, connectivity between communities, and neural connections in a brain. When all bit lines of the CBA are connected to the ground, the sneak current is suppressed, and the CBA can be used to search for adjacent nodes. This work demonstrates the physical calculation methods applied to various graphical problems using the CBA composed of the self-rectifying memristor based on the HfO2 switching layer. Moreover, such applications suffer less from the memristors' inherent issues related to their stochastic nature.
Keywords: crossbar-arrays; graph algorithms; process-in-memory; self-rectifying memristor; sneak current.
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