Terracost

Abstract

This paper addresses the problem of computing least-cost-path surfaces for massive grid terrains. Consider a grid terrain T and let C be a cost grid for T such that every point in C stores a value that represents the cost of traversing the corresponding point in T . Given C and a set of sources S ∈ T , a least-cost-path grid Δ for T is a grid such that every point in Δ represents the distance to the source in S that can be reached with minimal cost. We present a scalable approach to computing least-cost-path grids. Our algorithm, terracost, is derived from our previous work on I/O-efficient shortest paths on grids and uses O (sort( n )) I/Os, where sort( n ) is the complexity of sorting n items of data in the I/O-model of Aggarwal and Vitter. We present the design, the analysis, and an experimental study of terracost. An added benefit of the algorithm underlying terracost is that it naturally lends itself to parallelization. We have implemented terracost in a distributed environment using our cluster management tool and report on experiments that show that it obtains speedup near-linear with the size of the cluster. To the best of our knowledge, this is the first experimental evaluation of a multiple-source least-cost-path algorithm in the external memory setting.