The Node-Disjoint Paths Problem is given by an undirected graph G and k pairs of nodes (si, ti) for i = 1, … k. The problem is to decide whether there are node-disjoint paths Pi so that path Pi connects si to ti. Give a polynomial-time algorithm for the Node-Disjoint Paths Problem for the special case in which G has tree-width 2, and we are also given a tree decomposition T of G with width 2.
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