In this paper, we consider algorithms for maintaining treedecompositions with constant bounded treewidth under edge and vertex insertions and deletions for graphs with treewidth at most 2 (also called: partial 2-trees, or series-parallel graphs), and for almost trees with parameter k. Each operation can be performed in O(log n) time. For a large number of graph decision, optimization and counting problems, information can be maintained using O(log n) time per update, such that queries can be resolved in O(log n) or O(1) time. Similar results hold for the classes of almost trees with parameter k, for fixed k.
CITATION STYLE
Bodlaender, H. L. (1994). Dynamic algorithms for graphs with Treewidth 2. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 790 LNCS, pp. 112–124). Springer Verlag. https://doi.org/10.1007/3-540-57899-4_45
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