Developing algorithms and software for geometric path planning problems
ACM Computing Surveys (CSUR) - Special issue: position statements on strategic directions in computing research
On Geometric Path Query Problems
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
GIS: A Computing Perspective, 2nd Edition
GIS: A Computing Perspective, 2nd Edition
Modeling Costs of Turns in Route Planning
Geoinformatica
A fastest route planning for LBS based on traffic prediction
ICS'05 Proceedings of the 9th WSEAS International Conference on Systems
Simplest Instructions: Finding Easy-to-Describe Routes for Navigation
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Reducing the memory required to find a geodesic shortest path on a large mesh
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Easiest-to-reach neighbor search
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Optimal route determination technology based on trajectory querying moving object database
DEXA'06 Proceedings of the 17th international conference on Database and Expert Systems Applications
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Shortest path algorithms optimize the costs of a journey in a graph. The cost function may differ; in geometric contexts for instance the travel distance, the travel time, or travel expenses are considered. Not considered so far are costs that are related to the combination of incident edges for a path. For example, if one is interested in continuing a route from a given edge with the turn of least angle, each continuation by an incident edge has to be weighted by the angle enclosed. Such cost functions produce a combinatorial complex number of weights that cannot be stored with the edges or nodes in the graph. Instead they lead to an optimization problem in a linear dual graph, for which then a shortest path algorithm can be applied.This paper gives a motivation for this kind of costs, defines the linear dual graph, presents the route-planning algorithm, and discusses its properties. Examples from guidance of pedestrians in urban environment illustrate the results.