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Comparing Directed and Weighted Road Maps

  • Alyson Bittner
  • Brittany Terese FasyEmail author
  • Maia Grudzien
  • Sayonita Ghosh Hajra
  • Jici Huang
  • Kristine Pelatt
  • Courtney Thatcher
  • Altansuren Tumurbaatar
  • Carola Wenk
Chapter
Part of the Association for Women in Mathematics Series book series (AWMS, volume 13)

Abstract

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.

Notes

Acknowledgements

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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Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  • Alyson Bittner
    • 1
  • Brittany Terese Fasy
    • 2
    Email author
  • Maia Grudzien
    • 3
  • Sayonita Ghosh Hajra
    • 4
  • Jici Huang
    • 5
  • Kristine Pelatt
    • 6
  • Courtney Thatcher
    • 7
  • Altansuren Tumurbaatar
    • 8
  • Carola Wenk
    • 9
  1. 1.Department of MathematicsUniversity at Buffalo (SUNY)BuffaloUSA
  2. 2.Gianforte School of Computing and Department of Mathematical SciencesMontana State UniversityBozemanUSA
  3. 3.School of ComputingMontana State UniversityBozemanUSA
  4. 4.Department of MathematicsHamline UniversitySt PaulUSA
  5. 5.Gianforte School of ComputingMontana State UniversityBozemanUSA
  6. 6.Department of MathematicsSt. Catherine UniversitySt PaulUSA
  7. 7.Department of Mathematics and Computer ScienceUniversity of Puget SoundTacomaUSA
  8. 8.Department of Mathematics and StatisticsWashington State UniversityPullmanUSA
  9. 9.Department of Computer ScienceTulane UniversityNew OrleansUSA

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