Abstract
We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard parameterization, where the parameter is the difference |V(G)|−|V(H)|, with G and H being the larger and the smaller input graph, respectively. Intuitively, we can interpret this problem as “cleaning” the graph G, regarded as a pattern containing extra vertices indicating errors, in order to obtain the graph H representing the original pattern. We also prove W[1]-hardness for the standard parameterization where the parameter is |V(H)|.
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Notes
While we define modules in the standard way, our notion of closed modules is non-standard.
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Acknowledgement
Supported by the Hungarian National Research Fund OTKA 67651. Schlotter was also supported by the European Union and the European Social Fund (grant TÁMOP 4.2.1./B-09/1/KMR-2010-0003).
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Marx, D., Schlotter, I. Cleaning Interval Graphs. Algorithmica 65, 275–316 (2013). https://doi.org/10.1007/s00453-011-9588-0
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DOI: https://doi.org/10.1007/s00453-011-9588-0