Work

Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths

Year: 2026

Type: article

Abstract: We consider the classical single-source shortest path problem in directed weighted graphs. Eppstein proved recently an \(\Omega(n^{3})\) 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 \(\Omega(n^{3})\) lower bound to 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.

Source: ACM Transactions on Algorithms

DOI: 10.1145/3816151

Authors: Sunny Atalig, Alexander Hickerson, Arrdya Srivastav, Tingting Zheng, Marek Chrobak

Institutions: University of California, Riverside, Guangdong University of Technology

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

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