Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles

Authors Samir Datta, Kishlaya Jaiswal

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


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.

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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)


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
  • permanent mod powers of 2
  • parallel computation
  • graphs
  • shortest disjoint paths
  • shortest disjoint cycles


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