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Algorithm Engineering of SSSP with Negative Edge Weights

Authors Alejandro Cassis, Andreas Karrenbauer , André Nusser , Paolo Luigi Rinaldi

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  • Theory of computation → Shortest paths
Keywords
  • Single Source Shortest Paths
  • Negative Weights
  • Near-Linear Time

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Abstract

Computing shortest paths is one of the most fundamental algorithmic graph problems. It is known since decades that this problem can be solved in near-linear time if all weights are nonnegative. A recent break-through by [Aaron Bernstein et al., 2022] presented a randomized near-linear time algorithm for this problem. A subsequent improvement in [Karl Bringmann et al., 2023] significantly reduced the number of logarithmic factors and thereby also simplified the algorithm. It is surprising and exciting that both of these algorithms are combinatorial and do not contain any fundamental obstacles for being practical.
We launch the, to the best of our knowledge, first extensive investigation towards a practical implementation of [Karl Bringmann et al., 2023]. To this end, we give an accessible overview of the algorithm and discuss what adaptions are necessary to obtain a fast algorithm in practice. We manifest these adaptions in an efficient implementation. We test our implementation on a benchmark data set that is adapted to be more difficult for our implementation in order to allow for a fair comparison. As in [Karl Bringmann et al., 2023] as well as in our implementation there are multiple parameters to tune, we empirically evaluate their effect and thereby determine the best choices. Our implementation is then extensively compared to one of the state-of-the-art algorithms for this problem [Andrew V. Goldberg and Tomasz Radzik, 1993]. On the hardest instance type, we are faster by up to almost two orders of magnitude.

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Alejandro Cassis, Andreas Karrenbauer, André Nusser, and Paolo Luigi Rinaldi. Algorithm Engineering of SSSP with Negative Edge Weights. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.10

Author Details

Alejandro Cassis
  • Saarland University and Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
Andreas Karrenbauer
  • Max Planck Institute for Informatics and Saarland University, Saarland Informatics Campus, Saarbrücken, Germany
André Nusser
  • Université Côte d'Azur, CNRS, Inria, France
Paolo Luigi Rinaldi
  • Max Planck Institute for Informatics and Saarland University, Saarland Informatics Campus, Saarbrücken, Germany

Funding

  • Nusser, André: This work was supported by the French government through the France 2030 investment plan managed by the National Research Agency (ANR), as part of the Initiative of Excellence of Université Côte d'Azur under reference number ANR-15-IDEX-01.

Acknowledgements

We want to thank Karl Bringmann and Danupon Nanongkai for their helpful input.

Supplementary Materials

References

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