“切片”子窗口搜索：最大矩形问题的次线性复杂度解决方案
"Sliced" Subwindow Search: a Sublinear-complexity Solution to the Maximum Rectangle Problem
AI总结：
本文提出了一种针对最大矩形问题（子窗口搜索）的“切片”子窗口搜索方法，通过在矩阵等距切片间插值实现次线性时间和内存复杂度，在自然图像上以99%的准确率实现11倍速度与内存提升，适用于大规模矩阵和实时应用。
摘要：
考虑一个包含正数和负数的二维矩阵，如何在其内部绘制一个矩形，使得其包含元素的总和大于所有其他矩形？这个通常被称为最大矩形问题或子窗口搜索的基础问题，跨越了许多计算领域。然而，如果不要求计算资源至少与矩阵大小成线性比例，该问题一直未被解决。在本研究中，我们提出了一种解决该问题的新方法，通过在矩阵的少量等距切片之间进行插值，实现了次线性的时间和内存复杂度。应用于自然图像时，我们的解决方案以99%的相对准确率实现了11倍的速度和内存效率提升，从而超越了现有技术。通常，当矩阵足够大且可以接受准确率的微小下降时（例如在许多涉及自然图像的问题中），我们的解决方案优于现有方案。因此，它非常适合于实时应用以及最大矩形问题的各种计算困难实例。
英文摘要：
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow search, spans many computational domains. Yet, the problem has not been solved without demanding computational resources at least linearly proportional to the size of the matrix. In this work, we present a new approach to the problem which achieves sublinear time and memory complexities by interpolating between a small amount of equidistant sections of the matrix. Applied to natural images, our solution outperforms the state-of-the-art by achieving an 11x increase in speed and memory efficiency at 99% comparative accuracy. In general, our solution outperforms existing solutions when matrices are sufficiently large and a marginal decrease in accuracy is acceptable, such as in many problems involving natural images. As such, it is well-suited for real-time application and in a variety of computationally hard instances of the maximum rectangle problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
