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

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

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • single-source shortest paths
  • lower bounds
  • decision trees

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Abstract

We consider the classical single-source shortest path problem in directed weighted graphs. D. Eppstein proved recently an Ω(n³) 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) 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.

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Sunny Atalig, Alexander Hickerson, Arrdya Srivastav, Tingting Zheng, and Marek Chrobak. Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.8

Author Details

Sunny Atalig
  • University of California, Riverside, CA, USA
Alexander Hickerson
  • University of California, Riverside, CA, USA
Arrdya Srivastav
  • University of California, Riverside, CA, USA
Tingting Zheng
  • Guangdong University of Technology, Guangzhou, China
Marek Chrobak
  • University of California, Riverside, CA, USA

Funding

Research partially supported by National Science Foundation grant CCF-2153723.

References

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