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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422917" target="_blank" >RIV/00216208:11320/20:10422917 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.ICALP.2020.122" target="_blank" >https://doi.org/10.4230/LIPIcs.ICALP.2020.122</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2020.122" target="_blank" >10.4230/LIPIcs.ICALP.2020.122</a>

Result language
angličtina
Original language name
Dynamic Complexity of Reachability: How Many Changes Can We Handle?
Original language description
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.
Czech name
—
Czech description
—

Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
ISBN
978-3-95977-138-2
ISSN
1868-8969
e-ISSN
—
Number of pages
19
Pages from-to
1-19
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fur Informatik
Place of publication
Dagstuhl
Event location
Saarbrücken, Německo
Event date
Jul 8, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—

Similar results(10)