Parallel Privacy-Preserving Shortest Paths by Radius-Stepping

The radius-stepping algorithm is an efficient, parallelixable algorithm for finding the shortest paths in graphs. It solved the problem in Δ-Stepping algorithm, which has no known theoretical bounds fur general graphs. 1" this paper, we describe a parallel privacy-preserving method for finding SingleSource Shortest Paths (SSSP). Our optimized method is based on the Radius-Stepping algorithm. The method is implemented on iop of the Secure Multiparty Computation (SMC) Sharemiiid platform. We have reshaped the radius-stepping algorithm to work on vectors representing the graph in a SIMD manner, in order to enable a fast execution using the secret-sharing based SMC protocol set of Sharemind. The results of the real implementation show an efficient method that reduced the execution time hundreds of times iii comparison with a standard case of the privacy-preserving radius-stepping and Δ-Stepping algorithms.