License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.122
URN: urn:nbn:de:0030-drops-125291
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12529/
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Datta, Samir ; Kumar, Pankaj ; Mukherjee, Anish ; Tawari, Anuj ; Vortmeier, Nils ; Zeume, Thomas

Dynamic Complexity of Reachability: How Many Changes Can We Handle?

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LIPIcs-ICALP-2020-122.pdf (0.6 MB)

Abstract

In 2015, it was shown that reachability for arbitrary directed graphs can be updated by first-order formulas after inserting or deleting single edges. Later, in 2018, this was extended for changes of size (log n)/(log log n), where n is the size of the graph. Changes of polylogarithmic size can be handled when also majority quantifiers may be used.
In this paper we extend these results by showing that, for changes of polylogarithmic size, first-order update formulas suffice for maintaining (1) undirected reachability, and (2) directed reachability under insertions. For classes of directed graphs for which efficient parallel algorithms can compute non-zero circulation weights, reachability can be maintained with update formulas that may use "modulo 2" quantifiers under changes of polylogarithmic size. Examples for these classes include the class of planar graphs and graphs with bounded treewidth. The latter is shown here.
As the logics we consider cannot maintain reachability under changes of larger sizes, our results are optimal with respect to the size of the changes.

BibTeX - Entry

@InProceedings{datta_et_al:LIPIcs:2020:12529,
  author =	{Samir Datta and Pankaj Kumar and Anish Mukherjee and Anuj Tawari and Nils Vortmeier and Thomas Zeume},
  title =	{{Dynamic Complexity of Reachability: How Many Changes Can We Handle?}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{122:1--122:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12529},
  URN =		{urn:nbn:de:0030-drops-125291},
  doi =		{10.4230/LIPIcs.ICALP.2020.122},
  annote =	{Keywords: Dynamic complexity, reachability, complex changes}
}

Keywords: Dynamic complexity, reachability, complex changes
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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