Algebraic Dynamic Programming on Trees
AbstractWhere string grammars describe how to generate and parse strings, tree grammars describe how to generate and parse trees. We show how to extend generalized algebraic dynamic programming to tree grammars. The resulting dynamic programming algorithms are efficient and provide the complete feature set available to string grammars, including automatic generation of outside parsers and algebra products for efficient backtracking. The complete parsing infrastructure is available as an embedded domain-specific language in Haskell. In addition to the formal framework, we provide implementations for both tree alignment and tree editing. Both algorithms are in active use in, among others, the area of bioinformatics, where optimization problems on trees are of considerable practical importance. This framework and the accompanying algorithms provide a beneficial starting point for developing complex grammars with tree- and forest-based inputs. View Full-Text
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Berkemer, S.J.; Höner zu Siederdissen, C.; Stadler, P.F. Algebraic Dynamic Programming on Trees. Algorithms 2017, 10, 135.
Berkemer SJ, Höner zu Siederdissen C, Stadler PF. Algebraic Dynamic Programming on Trees. Algorithms. 2017; 10(4):135.Chicago/Turabian Style
Berkemer, Sarah J.; Höner zu Siederdissen, Christian; Stadler, Peter F. 2017. "Algebraic Dynamic Programming on Trees." Algorithms 10, no. 4: 135.
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