55 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Faster Parameterized Algorithms for Modification Problems to Minor-Closed Classes

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    Parameterized Graph Modification Beyond the Natural Parameter

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    Finding a Highly Connected Steiner Subgraph and its Applications

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    Given a (connected) undirected graph G, a set X ? V(G) and integers k and p, the Steiner Subgraph Extension problem asks whether there exists a set S ? X of at most k vertices such that G[S] is a p-edge-connected subgraph. This problem is a natural generalization of the well-studied Steiner Tree problem (set p = 1 and X to be the terminals). In this paper, we initiate the study of Steiner Subgraph Extension from the perspective of parameterized complexity and give a fixed-parameter algorithm (i.e., FPT algorithm) parameterized by k and p on graphs of bounded degeneracy (removing the assumption of bounded degeneracy results in W-hardness). Besides being an independent advance on the parameterized complexity of network design problems, our result has natural applications. In particular, we use our result to obtain new single-exponential FPT algorithms for several vertex-deletion problems studied in the literature, where the goal is to delete a smallest set of vertices such that: (i) the resulting graph belongs to a specified hereditary graph class, and (ii) the deleted set of vertices induces a p-edge-connected subgraph of the input graph

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Parameterized Graph Modification Beyond the Natural Parameter

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    A survey of parameterized algorithms and the complexity of edge modification

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    The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.publishedVersio

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    Parameterized Algorithms for Finding Large Sparse Subgraphs:Kernelization and Beyond

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    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum
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