Dynamic treewidth

04/04/2023

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by   Tuukka Korhonen, et al.

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We present a data structure that for a dynamic graph G that is updated by edge insertions and deletions, maintains a tree decomposition of G of width at most 6k+5 under the promise that the treewidth of G never grows above k. The amortized update time is O_k(2^√(log n)loglog n), where n is the vertex count of G and the O_k(·) notation hides factors depending on k. In addition, we also obtain the dynamic variant of Courcelle's Theorem: for any fixed property φ expressible in the 𝖢𝖬𝖲𝖮_2 logic, the data structure can maintain whether G satisfies φ within the same time complexity bounds. To a large extent, this answers a question posed by Bodlaender [WG 1993].