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Quickest known integer relation algorithm in the case of signs

Let $x_1,\cdots,x_n,k$ be integers such that $|k|\le\sum_{i=1}^n|x_i|$. What is the quickest known algorithm to determine $w_i\in\{-1,0,1\}$ such that $k=\sum_{i=1}^nw_ix_i$ where they exist? What is ...
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