Hierarchical Time-Dependent Oracles

TL;DR

This paper introduces hierarchical time-dependent oracles that efficiently compute shortest paths in networks with time-varying costs, achieving fast query times and low preprocessing costs regardless of the network's complexity.

Contribution

It presents novel hierarchical oracles for time-dependent networks with provable subquadratic preprocessing and sublinear query times, independent of the network's disconcavity.

Findings

Achieves subquadratic preprocessing time and space.

Provides sublinear query time in network size or Dijkstra-Rank.

Works independently of the network's disconcavity.

Abstract

We study networks obeying \emph{time-dependent} min-cost path metrics, and present novel oracles for them which \emph{provably} achieve two unique features: % (i) \emph{subquadratic} preprocessing time and space, \emph{independent} of the metric's amount of disconcavity; % (ii) \emph{sublinear} query time, in either the network size or the actual Dijkstra-Rank of the query at hand.