Comparing Directed and Weighted Road Maps
With the increasing availability of GPS trajectory data, map construction algorithms have been developed that automatically construct road maps from this data. In order to assess the quality of such (constructed) road maps, the need for meaningful road map comparison algorithms becomes increasingly important. Indeed, different approaches for map comparison have been recently proposed; however, most of these approaches assume that the road maps are modeled as undirected embedded planar graphs.
In this paper, we study map comparison algorithms for more realistic models of road maps: directed roads as well as weighted roads. In particular, we address two main questions: how close are the graphs to each other, and how close is the information presented by the graphs (i.e., traffic times, trajectories, and road type)? We propose new road network comparisons and give illustrative examples. Furthermore, our approaches do not only apply to road maps but can be used to compare other kinds of graphs as well.
This paper is the product of a working group of WinCompTop 2016, sponsored by NSF DMS 1619908, Microsoft Research, and the Institute for Mathematics and Its Applications (IMA) in Minneapolis, MN. In addition, part of this research was conducted under NSF CCF 618605 (Fasy) and NSF CCF 1618469 (Wenk).
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