Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths
Data Structures and Algorithms
2024-11-12 v1
Abstract
We consider the classical single-source shortest path problem in directed weighted graphs. D.~Eppstein proved recently an lower bound for oblivious algorithms that use relaxation operations to update the tentative distances from the source vertex. We generalize this result by extending this lower bound to \emph{adaptive} algorithms that, in addition to relaxations, can perform queries involving some simple types of linear inequalities between edge weights and tentative distances. Our model captures as a special case the operations on tentative distances used by Dijkstra's algorithm.
Cite
@article{arxiv.2411.06546,
title = {Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths},
author = {Sunny Atalig and Alexander Hickerson and Arrdya Srivastav and Tingting Zheng and Marek Chrobak},
journal= {arXiv preprint arXiv:2411.06546},
year = {2024}
}