A Parameterized Complexity View on Collapsing k-Cores

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00328474" target="_blank" >RIV/68407700:21240/19:00328474 - isvavai.cz</a>

Result on the web

<a href="http://drops.dagstuhl.de/opus/volltexte/2019/10208/" target="_blank" >http://drops.dagstuhl.de/opus/volltexte/2019/10208/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.IPEC.2018.7" target="_blank" >10.4230/LIPIcs.IPEC.2018.7</a>

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. [AAAI 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. We show that Collapsed k-Core is W[1]-hard when parameterized by b and in FPT when parameterized by (b+x) if k <=2. Furthermore, we show 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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Type

D - Article in proceedings

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)

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)

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

ISBN

978-3-95977-084-2

ISSN

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e-ISSN

1868-8969

Number of pages

14

Pages from-to

"7:1"-"7:14"

Publisher name

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Place of publication

Dagstuhl

Event location

Helsinky

Event date

Aug 22, 2018

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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