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New Additive Approximations for Shortest Paths and Cycles

Authors Mingyang Deng, Yael Kirkpatrick, Victor Rong , Virginia Vassilevska Williams, Ziqian Zhong

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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Fine-grained Complexity
  • Additive Approximation

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Abstract

This paper considers additive approximation algorithms for All-Pairs Shortest Paths (APSP) and Shortest Cycle in undirected unweighted graphs. The results are as follows:  
- We obtain the first +2-approximation algorithm for APSP in n-vertex graphs that improves upon Dor, Halperin and Zwick’s (SICOMP'00) Õ(n^{7/3}) time algorithm. The new algorithm runs in Õ(n^2.29) time and is obtained via a reduction to Min-Plus product of bounded difference matrices.
- We obtain the first additive approximation scheme for Shortest Cycle, generalizing the approximation algorithms of Itai and Rodeh (SICOMP'78) and Roditty and Vassilevska W. (SODA'12). For every integer r ≥ 0, we give an Õ(n+n^{2+r}/m^r) time algorithm that returns a +(2r+1)-approximate shortest cycle in any n-vertex, m-edge graph.

Cite As Get BibTex

Mingyang Deng, Yael Kirkpatrick, Victor Rong, Virginia Vassilevska Williams, and Ziqian Zhong. New Additive Approximations for Shortest Paths and Cycles. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 50:1-50:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ICALP.2022.50

Author Details

Mingyang Deng
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Yael Kirkpatrick
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Victor Rong
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Virginia Vassilevska Williams
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Ziqian Zhong
  • Massachusetts Institute of Technology, Cambridge, MA, USA

Funding

  • Vassilevska Williams, Virginia: Partially funded by NSF awards 2129139 and 1909429, BSF award 2020356, and a Google Research Fellowship.

References

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