(Preprint) Resonance Algorithm: A New Look at the Shortest Path Problem
Yu LIU 刘宇 ¹, Qiguang LIN 林麒光 ², Binbin HONG 洪斌斌 ³, Daniel HJERPE ⁴, Xiaofeng LIU 刘小峰 ² ⁵
¹ International Academic Center of Complex Systems, Beijing Normal University at Zhuhai, Zhuhai 519087, Guangdong, China
中国 广东 珠海 北京师范大学(珠海)复杂系统国际科学中心
² College of IoT Engineering, Hohai University, Changzhou 213022, Jiangsu, China
中国 江苏 常州 河海大学物联网工程学院
³ Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, Guangdong, China
中国 广东 深圳 深圳大学微纳光电子学研究院
⁴ Ericsson AB, Kista 16483, Sweden
⁵ Jiangsu Key laboratory of Special Robotic Technologies, Changzhou 213022, Jiangsu, China
中国 江苏 常州 江苏省特种机器人技术重点实验室
ChinaXiv, 2021-10-11

The shortest path problem (SPP) is a classic problem and appears in a wide range of applications. Although a variety of algorithms already exist, new advances are still being made, mainly tuned for particular scenarios to have better performances. As a result, they become more and more technically complex and sophisticated.

Here we developed a novel nature-inspired algorithm to compute all possible shortest paths between two nodes in a graph: Resonance Algorithm (RA), which is surprisingly simple and intuitive. Besides its simplicity, RA turns out to be much more time-efficient for large-scale graphs than the extended Dijkstra's algorithm (such that it gives all possible shortest paths).

Moreover, RA can handle any undirected, directed, or mixed graphs, irrespective of loops, unweighted or positively-weighted edges, and can be implemented in a fully decentralized manner. These good properties ensure RA a wide range of applications.
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