A Parameterized Complexity View on Collapsing k-Cores
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F21%3A00354097" target="_blank" >RIV/68407700:21240/21:00354097 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00224-021-10045-w" target="_blank" >https://doi.org/10.1007/s00224-021-10045-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00224-021-10045-w" target="_blank" >10.1007/s00224-021-10045-w</a>
Alternative languages
Result language
angličtina
Original language name
A Parameterized Complexity View on Collapsing k-Cores
Original language description
We study the NP-hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced subgraph with minimum degree k, has size at most x. Collapsed k-Core was introduced by Zhang et al. (2017) and it is motivated by the study of engagement behavior of users in a social network and measuring the resilience of a network against user drop outs. Collapsed k-Core is a generalization of r-Degenerate Vertex Deletion (which is known to be NP-hard for all r >= 0) where, given an undirected graph G and integers b and r, we are asked to remove b vertices such that the remaining graph is r-degenerate, that is, every its subgraph has minimum degree at most r. We investigate the parameterized complexity of Collapsed k-Core with respect to the parameters b, x, and k, and several structural parameters of the input graph. We reveal a dichotomy in the computational complexity of Collapsed k-Core for k <= 2 and k >= 3. For the latter case it is known that for all x >= 0 Collapsed k-Core is W[P]-hard when parameterized by b. For k <= 2 we show that Collapsed k-Core is W[1]-hard when parameterized by b and in FPT when parameterized by (b + x). Furthermore, we outline that Collapsed k-Core is in FPT when parameterized by the treewidth of the input graph and presumably does not admit a polynomial kernel when parameterized by the vertex cover number of the input graph.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA17-20065S" target="_blank" >GA17-20065S: Tight Parameterized Results for Directed Connectivity Problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Theory of Computing Systems
ISSN
1432-4350
e-ISSN
1433-0490
Volume of the periodical
65
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
40
Pages from-to
1243-1282
UT code for WoS article
000663468900002
EID of the result in the Scopus database
2-s2.0-85108313727