# Deriving New Minimum Cost Pathways from Existing Paths

By Dean, Denis J. | Cartography and Geographic Information Science, January 2005 | Go to article overview

# Deriving New Minimum Cost Pathways from Existing Paths

Dean, Denis J., Cartography and Geographic Information Science

Introduction

Geographic Information System (GIS) "based cost spreading techniques are widely used to find minimum cost paths from specified starting point(s) to specified ending point(s). These raster-based techniques assume that the costs of traversing each raster cell within the area of interest are known. In general, cost spreading algorithms require as inputs:

* The locations of the starting and ending point(s);

* A raster database that describes the cost of traversing each raster cell in the study area; and in the case of anisotropic costs;

* Additional databases and/or mechanisms that allow the cell traversing costs to be modified to account for the direction of travel.

The output of cost-spreading analysis is typically a new raster database showing the minimum-cost path connecting the starting point/ending point pair that produces the smallest total traversing cost of all possible pairs of starting and ending points. The cost-spreading algorithms that generate these outputs employ a form of dynamic programming, which offers a reliable and relatively efficient way of solving what on its surface appears to be a fairly formidable problem (Huriot et al. 1989; Smith 1989).

This study presents a technique for estimating traversing costs from an existing minimum cost path. It is assumed that an existing minimum cost path is present and that the components of traversing costs are known (e.g., road-building costs may be a function of slope, gradient and soil type), and that traversing costs are a linear combination of their component costs (e.g., road-building costs from the previous example could be computed as a linear function of slope, gradient, and soil type). Unknown will be the parameters of the linear equation that constructs traversing costs from its components. I will start by presenting techniques for estimating these parameters in the isotropic case. I will then extend these techniques to include the anisotropic case. Both cases will be illustrated using example problems.

Case 1: Isotropic Traversing Costs

Assume that a minimum cost path exists from starting point [P.

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