The suitability of the weighted lp-norm in estimating actual road distances

Abstract

The weighted l p -norm, suggested as a way to estimate actual road distances, takes time and effort to calculate because it requires two parameters. Compared to the weighted Euclidean norm, a function requiring only one parameter which is relatively easy to obtain, the weighted l p -norm yields considerably better estimates for some countries and only negligible improvements for others. This paper evaluates whether, on the basis of easy-to-obtain data characterizing the road network of a particular area, one can predict the extent of the improvement in estimate accuracy. Such an ability to predetermine estimate accuracy would help researchers decide when to use the expensive l p -norm. The investigation shows, however, that no such relationship can be proven. The extent of the improvement in estimate accuracy offered by the weighted l p -norm cannot be predicted.