Route Specifications with a Linear Dual Graph

Abstract

The objective often explored in Web-based route planners is to find an optimal route in a network for a given mode of transport. Usually this involves searching for the cheapest route corresponding to some cost function. For many types of trips, not all desired route properties can be satisfied in this way. Following is a proposed solution for planning hiking trips. The method can easily be transferred to tourist guides in urban areas, for advice for taking a drive, or can be used in related contexts. It is anticipated that these applications will become increasingly relevant in our mobile leisure society.

Planning a hiking route is based primarily on the intended length of the trip, and then on the decision about whether start and destination points need to coincide. As a result, planning trips represents neither a shortest path nor a travelling salesman problem.

The problem with this approach lies in the fact that hikers require trip proposals that cannot necessarily be provided by a shortest path algorithm: round tours, routes including loops, or routes where a route segment which has to be passed in both directions are more consistent with route planning for hikers. A surprisingly simple solution for these requirements appears to be a linear dual graph, which applies a k shortest path algorithm to the linear dual graph. This paper outlines this approach and demonstrates that it achieves realistic and practical route planning.