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- W4385774088 abstract "We study a generalization of the classic Spanning Tree problem that allows for a non-uniform failure model. More precisely, edges are either emph{safe} or emph{unsafe} and we assume that failures only affect unsafe edges. In Unweighted Flexible Graph Connectivity we are given an undirected graph $G = (V,E)$ in which the edge set $E$ is partitioned into a set $S$ of safe edges and a set $U$ of unsafe edges and the task is to find a set $T$ of at most $k$ edges such that $T - {u}$ is connected and spans $V$ for any unsafe edge $u in T$. Unweighted Flexible Graph Connectivity generalizes both Spanning Tree and Hamiltonian Cycle. We study Unweighted Flexible Graph Connectivity in terms of fixed-parameter tractability (FPT). We show an almost complete dichotomy on which parameters lead to fixed-parameter tractability and which lead to hardness. To this end, we obtain FPT-time algorithms with respect to the vertex deletion distance to cluster graphs and with respect to the treewidth. By exploiting the close relationship to Hamiltonian Cycle, we show that FPT-time algorithms for many smaller parameters are unlikely under standard parameterized complexity assumptions. Regarding problem-specific parameters, we observe that Unweighted Flexible Graph Connectivity} admits an FPT-time algorithm when parameterized by the number of unsafe edges. Furthermore, we investigate a below-upper-bound parameter for the number of edges of a solution. We show that this parameter also leads to an FPT-time algorithm." @default.
- W4385774088 created "2023-08-12" @default.
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- W4385774088 date "2023-08-08" @default.
- W4385774088 modified "2023-10-18" @default.
- W4385774088 title "On the Complexity of Finding a Sparse Connected Spanning Subgraph in a non-Uniform Failure Model" @default.
- W4385774088 doi "https://doi.org/10.48550/arxiv.2308.04575" @default.
- W4385774088 hasPublicationYear "2023" @default.
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