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You are given a tree decomposition of a large graph with not so small bounded tree-width.

Suppose now you need to solve a dynamic programming problem inside a subgraph and does not have time to do another costly tree decomposition.

How do I find the tree decomposition of a subgraph given the decomposition of its "father" graph?

(I googled for some data structure inside each bag of the tree decomposition but I haven't found anything.)

Thanks in advance.

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