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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%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>

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. [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

  • Czech description

Classification

  • 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)

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

    2019

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

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

  • ISBN

    978-3-95977-084-2

  • ISSN

  • 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