License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.36
URN: urn:nbn:de:0030-drops-144763
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14476/
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Datta, Samir ; Jaiswal, Kishlaya

Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles

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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.

BibTeX - Entry

@InProceedings{datta_et_al:LIPIcs.MFCS.2021.36,
  author =	{Datta, Samir and Jaiswal, Kishlaya},
  title =	{{Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14476},
  URN =		{urn:nbn:de:0030-drops-144763},
  doi =		{10.4230/LIPIcs.MFCS.2021.36},
  annote =	{Keywords: permanent mod powers of 2, parallel computation, graphs, shortest disjoint paths, shortest disjoint cycles}
}

Keywords: permanent mod powers of 2, parallel computation, graphs, shortest disjoint paths, shortest disjoint cycles
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021

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