Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Parameterized Complexity
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In this paper, we deal with restoring missing information in molecule databases: Some data formats only store the atoms' configuration but omit bond multiplicities. As this information is essential for various applications in chemistry, we consider the problem of recovering bond type information using a scoring function for the possible valences of each atom--the Bond Type Assignment problem. We prove the NP-hardness of Bond Type Assignment and give an exact fixed-parameter algorithm for the problem where bond types are computed via dynamic programming on a tree decomposition of the molecule graph. We evaluate our algorithm on a set of real molecule graphs and find that it works fast and accurately.