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.IPEC.2018.7
URN: urn:nbn:de:0030-drops-102088
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10208/
Luo, Junjie ;
Molter, Hendrik ;
Suchý, Ondrej
A Parameterized Complexity View on Collapsing k-Cores
Abstract
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.
BibTeX - Entry
@InProceedings{luo_et_al:LIPIcs:2019:10208,
author = {Junjie Luo and Hendrik Molter and Ondrej Such{\'y}},
title = {{A Parameterized Complexity View on Collapsing k-Cores}},
booktitle = {13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
pages = {7:1--7:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-084-2},
ISSN = {1868-8969},
year = {2019},
volume = {115},
editor = {Christophe Paul and Michal Pilipczuk},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10208},
URN = {urn:nbn:de:0030-drops-102088},
doi = {10.4230/LIPIcs.IPEC.2018.7},
annote = {Keywords: r-Degenerate Vertex Deletion, Feedback Vertex Set, Fixed-Parameter Tractability, Kernelization Lower Bounds, Graph Algorithms, Social Network Analysis}
}
|
Keywords: |
|
r-Degenerate Vertex Deletion, Feedback Vertex Set, Fixed-Parameter Tractability, Kernelization Lower Bounds, Graph Algorithms, Social Network Analysis |
|
Collection: |
|
13th International Symposium on Parameterized and Exact Computation (IPEC 2018) |
|
Issue Date: |
|
2019 |
|
Date of publication: |
|
05.02.2019 |
