On Solving Floating Point SSSP Using an Integer Priority Queue

Abstract: We address the single source shortest path planning problem (SSSP) in the case of floating point edge weights. We show how any integer based Dijkstra solution that relies on a monotone integer priority queue to create a full ordering over path lengths in order to solve integer SSSP can be used as an oracle to solve floating point SSSP with positive edge weights (floating point P-SSSP). Floating point P-SSSP is of particular interest to the robotics community. This immediately yields a handful of faster runtimes for floating point P-SSSP; for example, ${O({m + n\log \log \frac{C}{\delta}})}$, where $C$ is the largest weight and $\delta$ is the minimum edge weight in the graph. It also ensures that many future advances for integer SSSP will be transferable to floating point P-SSSP.