English

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 Ω(n3)\Omega(n^3) 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 Ω(n3)\Omega(n^3) 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.

Keywords

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}
}
R2 v1 2026-06-28T19:54:52.231Z