Titlebook: Algorithms and Data Structures; 17th International S Anna Lubiw,Mohammad Salavatipour,Meng He Conference proceedings 2021 Springer Nature S

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On the Spanning and Routing Ratios of the Directed ,-Graph,tric graphs, no bound is known on the spanning and routing ratios of the directed .-graph. We show that the directed .-graph of a point set ., denoted ., is a 7-spanner and there exist point sets where the spanning ratio is at least ., for any .. It is known that the standard greedy .-routing algori

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Pattern Matching in Doubling Spaces,tant doubling dimension .. More precisely, given an input parameter ., the .-distortion problem is to find a one-to-one mapping from . to . that distorts distances by a factor at most .. We first show by a reduction from .-clique that, in doubling dimension ., this problem is NP-hard and W[1]-hard.

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