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Exploring spatial networks with greedy navigators

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Exploring spatial networks with greedy navigators

  1. 1. Petter HolmeUmeå University, Sungkyunkwan University,Stockholm University, Institute for Future StudiesSang Hoon LeeUmeå University, Oxford University
  2. 2. How can we measurenavigability?What does optimallynavigable networks looklike?
  3. 3. Full informationShortest paths
  4. 4. 3 t 4 62 51 8 7 s 9
  5. 5. 3 t 4 62 51 8 7 s 9
  6. 6. 3 t 4 62 51 8 7 s 9
  7. 7. 3 t 4 62 51 8 7 s 9
  8. 8. 3 t 4 62 51 8 7 s 9
  9. 9. Partial informationGreedy navigators
  10. 10. 3 t 4 62 51 8 7 s 9
  11. 11. 3 t 4 62 51 8 7 s 9
  12. 12. 3 t 4 62 51 8 7 s 9
  13. 13. 3 t 4 62 51 8 7 s 9
  14. 14. 3 t 4 62 51 8 7 s 9
  15. 15. 3 t 4 62 51 8 7 s 9
  16. 16. 3 t 4 62 51 8 7 s 9
  17. 17. (Greedy navigator) navigability Avg. distanceRg = Avg. distance for greedy navigators
  18. 18. (Greedy navigator) navigability Avg. distanceRg = Avg. distance for random navigators random navigators perform a random DFS
  19. 19. Rg = 33% Rr = 24%
  20. 20. Network N M dg d dr Rg RrBoston* 88 155 6.8 5.7 30.8 84% 19%null 8.6 3.7 23.2 43% 16%modelNew 125 217 8.3 6.8 44.4 82% 15%York*null 11.7 4.0 33.5 34% 12%modelLCM 184 194 62.8 20.6 86.2 33% 24%* from Youn, Gastner, Jeong, PRL (2008)
  21. 21. Navigator essentiality
  22. 22. 0 –2 –41 –6 –8 ln |e| –5 2 4 –6 3 –7 –8
  23. 23. 1 02 –5 3 –10 4 ln |e| –5 –6 –7
  24. 24. Optimizing spatial networkfor greedy navigators Fixed vertices, growing
  25. 25. Boston roads
  26. 26. MST
  27. 27. graph distance
  28. 28. Euclidean distance
  29. 29. Optimizing spatial networkfor greedy navigators Fixed vertices
  30. 30. Optimizing spatial networkfor greedy navigators Not fixed vertices
  31. 31. 0.2 BAdeviation from shortest path 0 optimized HK WS –0.2 Karate Club 2D square –0.4 1D ring –0.6 –0.8 –1 –1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 relative position f in greedy paths
  32. 32. 0.2deviation from shortest path BA 0 KK HK WS –0.2 Karate Club 2D square –0.4 1D ring –0.6 –0.8 –1 –1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 relative position f in GSN paths
  33. 33. Thank you!SH Lee & P Holme, 2012. Exploring maps with greedynavigators. Phys. Rev. Lett. 108:128701.SH Lee & P Holme, 2012. A greedy-navigatorapproach to navigable city plans. To appear in Eur.J. Phys. Spec. Top.SH Lee & P Holme, 2012. Geometric properties ofgraph layouts optimized for greedy navigation.Under review Phys. Rev. E.

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