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

$n$: 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