Abstract
The formalism of monadic second-order (MS) logic has been very successful in unifying a large number of algorithms for graphs of bounded treewidth. We extend the elegant framework of MS logic from static problems to dynamic problems, in which queries about MS properties of a graph of bounded treewidth are interspersed with updates of vertex and edge labels. This allows us to unify and occasionally strengthen a number of scattered previous results obtained in an ad-hoc manner and to enable solutions to a wide range of additional problems to be derived automatically.
As an auxiliary result of independent interest, we dynamize a data structure of Chazelle and Alon and Schieber for answering queries about sums of labels along paths in a tree with edges labeled by elements of a semigroup.
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Hagerup, T. (1997). Dynamic algorithms for graphs of bounded treewidth. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_186
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DOI: https://doi.org/10.1007/3-540-63165-8_186
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