Parameterized Complexity of the Anchored k-Core Problem for Directed Graphs

Chitnis, Rajesh; Fomin, Fedor V.; Golovach, Petr A.

doi:10.4230/LIPIcs.FSTTCS.2013.79

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Parameterized Complexity of the Anchored k-Core Problem for Directed Graphs

Authors Rajesh Chitnis, Fedor V. Fomin, Petr A. Golovach

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2013-12-10

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DOI: 10.4230/LIPIcs.FSTTCS.2013.79
URN: urn:nbn:de:0030-drops-43636

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Parameterized complexity
directed graphs
anchored $k$-core

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Abstract

We consider the Directed Anchored k-Core problem, where the task is for a given directed graph G and integers b, k and p, to find an induced subgraph H with at least p vertices (the core) such that all but at most b vertices (the anchors) of H have in-degree at least k. For undirected graphs, this problem was introduced by Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012]. We undertake a
systematic analysis of the computational complexity of Directed Anchored k-Core and show that:
- The decision version of the problem is NP-complete for every k>=1 even if the input graph is restricted to be a planar directed acyclic graph of maximum degree at most k+2.
- The problem is fixed parameter tractable (FPT) parameterized by the size of the core p for k=1, and W[1]-hard for k>=2.
- When the maximum degree of the graph is at most Delta, the problem is FPT parameterized by p+Delta if k>=Delta/2.

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Rajesh Chitnis, Fedor V. Fomin, and Petr A. Golovach. Parameterized Complexity of the Anchored k-Core Problem for Directed Graphs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 79-90, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013) https://doi.org/10.4230/LIPIcs.FSTTCS.2013.79

Author Details

Rajesh Chitnis

Fedor V. Fomin

Petr A. Golovach

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