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Kim, Julia Chuzhoy, Rachit Nimavat","submitted_at":"2018-05-25T03:01:00Z","abstract_excerpt":"We study the classical Node-Disjoint Paths (NDP) problem: given an undirected $n$-vertex graph G, together with a set {(s_1,t_1),...,(s_k,t_k)} of pairs of its vertices, called source-destination, or demand pairs, find a maximum-cardinality set of mutually node-disjoint paths that connect the demand pairs. The best current approximation for the problem is achieved by a simple greedy $O(\\sqrt{n})$-approximation algorithm.\n  A special case of the problem called NDP-Grid, where the underlying graph is a grid, has been studied extensively. 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