The Complexity of Linear Dependence Problems in Vector Spaces

@inproceedings{Bhattacharyya2011TheCO,
  title={The Complexity of Linear Dependence Problems in Vector Spaces},
  author={Arnab Bhattacharyya and Piotr Indyk and David P. Woodruff and Ning Xie},
  booktitle={ICS},
  year={2011}
}
We study extensions of the k-SUM problem to vector spaces over finite fields. Given a subset S ⊆ Fq of size r ≤ q, an integer k, 2 ≤ k ≤ n, and a vector v ∈ (Fq \ {0}), we define the TARGETSUM problem to be the problem of finding k elements xi1 , . . . , xik ∈ S for which ∑k j=1 vjxij = z, where z may either be an input or a fixed vector. We also study a variant of this, where instead of finding xi1 , . . . , xik ∈ S for which ∑k j=1 vjxij = z, we require that z be in span(xi1 , . . . , xik… CONTINUE READING

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