Simple I/O-efficient flow accumulation on grid terrains

TL;DR

This paper presents a simple, highly I/O-efficient algorithm for flow accumulation on grid terrains, significantly outperforming previous methods in terms of input/output operations.

Contribution

The authors introduce a new algorithm that solves the flow accumulation problem in O(scan(N)) I/Os, improving efficiency over prior O(sort(N)) I/O algorithms.

Findings

Algorithm achieves O(scan(N)) I/Os for flow accumulation.

Potentially an order of magnitude faster than previous methods.

Efficient for large grid terrains with minimal I/O operations.

Abstract

The flow accumulation problem for grid terrains takes as input a matrix of flow directions, that specifies for each cell of the grid to which of its eight neighbours any incoming water would flow. The problem is to compute, for each cell c, from how many cells of the terrain water would reach c. We show that this problem can be solved in O(scan(N)) I/Os for a terrain of N cells. Taking constant factors in the I/O-efficiency into account, our algorithm may be an order of magnitude faster than the previously known algorithm that is based on time-forward processing and needs O(sort(N)) I/Os.