On Solving Floating Point SSSP Using an Integer Priority Queue

TL;DR

This paper demonstrates how integer-based Dijkstra algorithms with monotone priority queues can be adapted to efficiently solve floating point single source shortest path problems with positive weights, benefiting robotics applications.

Contribution

It introduces a method to leverage integer SSSP solutions for floating point cases, enabling faster algorithms and transferability of future integer SSSP improvements.

Findings

Faster runtime complexity ${O({m + n ext{log} ext{log} rac{C}{ ext{delta}}})$ for floating point P-SSSP.

Transferability of integer SSSP advances to floating point scenarios.

Applicability to robotics and other domains with floating point edge weights.

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.