In spatial analysis and geographic information systems, cost distance analysis or cost path analysis is a method for determining one or more optimal routes of travel through unconstrained (two-dimensional) space.[1] The optimal solution is that which minimizes the total cost of the route, based on a field of cost density (cost per linear unit) that varies over space due to local factors. It is thus based on the fundamental geographic principle of Friction of distance. It is an optimization problem with multiple deterministic algorithm solutions, implemented in most GIS software.
The various problems, algorithms, and tools of cost distance analysis operate over an unconstrained two-dimensional space, meaning that a path could be of any shape. Similar cost optimization problems can also arise in a constrained space, especially a one-dimensional linear network such as a road or telecommunications network. Although they are similar in principle, the problems in network space require very different (usually simpler) algorithms to solve, largely adopted from graph theory. The collection of GIS tools for solving these problems are called network analysis.