The impact of parameterized complexity to interdisciplinary problem solving
The Multivariate Algorithmic Revolution and Beyond
Constrained multilinear detection for faster functional motif discovery
Information Processing Letters
Finding approximate and constrained motifs in graphs
Theoretical Computer Science
RANGI: A Fast List-Colored Graph Motif Finding Algorithm
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We study the NP-hard List-Colored Graph Motif problem which, given an undirected list-colored graph G=(V,E) and a multiset M of colors, asks for maximum-cardinality sets S\subseteq V and M^{\prime }\subseteq M such that G[S] is connected and contains exactly (with respect to multiplicity) the colors in M^{\prime }. List-Colored Graph Motif has applications in the analysis of biological networks. We study List-Colored Graph Motif with respect to three different parameterizations. For the parameters motif size \vert M\vert and solution size \vert S\vert, we present fixed-parameter algorithms, whereas for the parameter \vert V\vert -\vert M\vert, we show W[1]-hardness for general instances and achieve fixed-parameter tractability for a special case of List-Colored Graph Motif. We implemented the fixed-parameter algorithms for parameters \vert M\vert and \vert S\vert, developed further speed-up heuristics for these algorithms, and applied them in the context of querying protein-interaction networks, demonstrating their usefulness for realistic instances. Furthermore, we show that extending the request for motif connectedness to stronger demands, such as biconnectedness or bridge-connectedness leads to W[1]-hard problems when the parameter is the motif size \vert M\vert