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Creators/Authors contains: "Tani, Erasmo"

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  1. ; ; ; (, ICML'24: Proceedings of the 41st International Conference on Machine Learning)
    Accepted Manuscript Full Text Available
  2. ; ; (, Schloss Dagstuhl – Leibniz-Zentrum fΓΌr Informatik)
    Bringmann, Karl; Grohe, Martin; Puppis, Gabriele; Svensson, Ola (Ed.)
    We present polylogarithmic approximation algorithms for variants of the Shortest Path, Group Steiner Tree, and Group ATSP problems with vector costs. In these problems, each edge e has a vector cost c_e ∈ ℝ_{β‰₯0}^𝓁;. For a feasible solution - a path, subtree, or tour (respectively) - we find the total vector cost of all the edges in the solution and then compute the 𝓁_p-norm of the obtained cost vector (we assume that p β‰₯ 1 is an integer). Our algorithms for series-parallel graphs run in polynomial time and those for arbitrary graphs run in quasi-polynomial time. To obtain our results, we introduce and use new flow-based Sum-of-Squares relaxations. We also obtain a number of hardness results. 
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