2D Maximum Subarray (Maximum Subarray Problem)
Revision as of 10:23, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:2D Maximum Subarray (Maximum Subarray Problem)}} == Description == Given an $n \times n$ matrix $A$ of integers, find $i, j, k,l \in (n)$ with $i \leq j, k \leq l$ maximizing $\sum^j_{x=i}\sum^l_{y=k}A(x,y)$, that is, find a contiguous subarray of $A$ of maximum sum == Related Problems == Generalizations: Maximum Subarray Related: 1D Maximum Subarray, Maximum Square Subarray == Parameters == <pre>n: dimension of array</pre> == Table o...")
Description
Given an $n \times n$ matrix $A$ of integers, find $i, j, k,l \in (n)$ with $i \leq j, k \leq l$ maximizing $\sum^j_{x=i}\sum^l_{y=k}A(x,y)$, that is, find a contiguous subarray of $A$ of maximum sum
Related Problems
Generalizations: Maximum Subarray
Related: 1D Maximum Subarray, Maximum Square Subarray
Parameters
n: dimension of array
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Negative Triangle Detection | if: to-time: $O(n^{3-\epsilon})$ on $n\times n$ matrices then: from-time: $O(n^{3-\epsilon})$ on $n$ vertex graphs |
2016 | https://arxiv.org/pdf/1602.05837.pdf | link |
| Weighted, Undirected APSP | if: to-time: $O(n^{3-\epsilon})$ on $n\times n$ matrices then: from-time: $O(n^{3-\epsilon/{1}0})$ on $n$ vertex graphs |
2016 | https://arxiv.org/pdf/1602.05837.pdf | link |
References/Citation
https://www.sciencedirect.com/science/article/pii/S1571066104003135?via%3Dihub