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Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles

Authors Samir Datta, Kishlaya Jaiswal

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Author Details

Samir Datta
  • Chennai Mathematical Institute, India
Kishlaya Jaiswal
  • Chennai Mathematical Institute, India

Funding

  • Datta, Samir: Partially funded by a grant from Infosys foundation and SERB-MATRICS grant MTR/2017/000480.

Acknowledgements

We would like to thank Eric Allender for a discussion regarding what was known about field operations in ⨁L. We would also like to thank Partha Mukhopadhyay for his comments on a preliminary version of the paper. We thank the anonymous referees for helping us improve the presentation of the paper.

Cite As Get BibTex

Samir Datta and Kishlaya Jaiswal. Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.MFCS.2021.36

Abstract

We present a parallel algorithm for permanent mod 2^k of a matrix of univariate integer polynomials. It places the problem in ⨁L ⊆ NC². This extends the techniques of Valiant [Leslie G. Valiant, 1979], Braverman, Kulkarni and Roy [Mark Braverman et al., 2009] and Björklund and Husfeldt [Andreas Björklund and Thore Husfeldt, 2019] and yields a (randomized) parallel algorithm for shortest two disjoint paths improving upon the recent (randomized) polynomial time algorithm [Andreas Björklund and Thore Husfeldt, 2019].
We also recognize the disjoint paths problem as a special case of finding disjoint cycles, and present (randomized) parallel algorithms for finding a shortest cycle and shortest two disjoint cycles passing through any given fixed number of vertices or edges.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parallel algorithms
Keywords
  • permanent mod powers of 2
  • parallel computation
  • graphs
  • shortest disjoint paths
  • shortest disjoint cycles

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