Integer Relation Among Integers: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Integer Relation Among Integers (Integer Relation)}} == Description == Given a vector $x \in \mathbb{Z}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$ == Related Problems == Generalizations: Integer Relation Among Reals == Parameters == <pre>n: dimensionality of vectors</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Ti...") |
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== Parameters == | == Parameters == | ||
$n$: dimensionality of vectors | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[HJLS algorithm ( Integer Relation)|HJLS algorithm]] || 1986 || $O(n^{3}(n+k)$ | | [[HJLS algorithm ( Integer Relation)|HJLS algorithm]] || 1986 || $O(n^{3}(n+k))$ || $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable || Exact || Deterministic || [https://epubs-siam-org.ezproxy.canberra.edu.au/doi/pdf/10.1137/0218059 Time] | ||
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Latest revision as of 08:24, 10 April 2023
Description
Given a vector $x \in \mathbb{Z}^n$, find an integer relation, i.e. a non-zero vector $m \in \mathbb{Z}^n$ such that $<x, m> = 0$
Related Problems
Generalizations: Integer Relation Among Reals
Parameters
$n$: dimensionality of vectors
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| HJLS algorithm | 1986 | $O(n^{3}(n+k))$ | $O(n^{2})$ -- but requires infinite precision with large n or else it becomes unstable | Exact | Deterministic | Time |