# 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

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 10 CITATIONS

## On the parameterized complexity of k-SUM

• ArXiv
• 2013
VIEW 3 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

## An iterative method for linear decomposition of index generating functions

• Cryptography and Communications
• 2019
VIEW 1 EXCERPT
CITES BACKGROUND

## Bootstrapping of FHE over the Integers with Large Message Space

• Security and Communication Networks
• 2018
VIEW 1 EXCERPT

## Faster Bootstrapping of FHE over the Integers

• IACR Cryptology ePrint Archive
• 2017
VIEW 1 EXCERPT

• MFCS
• 2017

• SODA
• 2017

• Algorithmica
• 2014
VIEW 1 EXCERPT
CITES BACKGROUND

## 3SUM, 3XOR, Triangles

• Electronic Colloquium on Computational Complexity
• 2013

## Losing Weight by Gaining Edges

• ESA
• 2013
VIEW 1 EXCERPT
CITES BACKGROUND

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 48 REFERENCES

## On the Possibility of Faster SAT Algorithms

• SODA
• 2010
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Finding, Minimizing, and Counting Weighted Subgraphs

• SIAM J. Comput.
• 2013
VIEW 1 EXCERPT

## On a class of O(n2) problems in computational geometry

• Comput. Geom.
• 2012
VIEW 1 EXCERPT

VIEW 1 EXCERPT

• SODA
• 2010
VIEW 1 EXCERPT

## Green's Conjecture and Testing Linear Invariant Properties

• Property Testing
• 2010
VIEW 3 EXCERPTS

## Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal

• ACM Trans. Algorithms
• 2010
VIEW 1 EXCERPT

VIEW 1 EXCERPT

## On proper secrets, (t, k)-bases and linear codes

• Des. Codes Cryptogr.
• 2009
VIEW 1 EXCERPT

## Villar . On proper secrets , ( t , k )bases and linear codes

Alexander Vardy.
• Des . Codes Cryptography
• 2009