Data-oblivious graph algorithms for secure computation and outsourcing

Abstract

This work treats the problem of designing data-oblivious algorithms for classical and widely used graph problems. A data-oblivious algorithm is defined as having the same sequence of operations regardless of the input data and data-independent memory accesses. Such algorithms are suitable for secure processing in outsourced and similar environments, which serves as the main motivation for this work. We provide data-oblivious algorithms for breadth-first search, single-source single-destination shortest path, minimum spanning tree, and maximum flow, the asymptotic complexities of which are optimal, or close to optimal, for dense graphs.