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Exploring spatial networks with greedy navigators

  1. 1. Petter Holme Umeå University, Sungkyunkwan University, Stockholm University, Institute for Future Studies Sang Hoon Lee Umeå University, Oxford University
  2. 2. How can we measure navigability? What does optimally navigable networks look like?
  3. 3. Full information Shortest paths
  4. 4. 3 t 4 6 2 5 1 8 7 s 9
  5. 5. 3 t 4 6 2 5 1 8 7 s 9
  6. 6. 3 t 4 6 2 5 1 8 7 s 9
  7. 7. 3 t 4 6 2 5 1 8 7 s 9
  8. 8. 3 t 4 6 2 5 1 8 7 s 9
  9. 9. Partial information Greedy navigators
  10. 10. 3 t 4 6 2 5 1 8 7 s 9
  11. 11. 3 t 4 6 2 5 1 8 7 s 9
  12. 12. 3 t 4 6 2 5 1 8 7 s 9
  13. 13. 3 t 4 6 2 5 1 8 7 s 9
  14. 14. 3 t 4 6 2 5 1 8 7 s 9
  15. 15. 3 t 4 6 2 5 1 8 7 s 9
  16. 16. 3 t 4 6 2 5 1 8 7 s 9
  17. 17. (Greedy navigator) navigability Avg. distance Rg = Avg. distance for greedy navigators
  18. 18. (Greedy navigator) navigability Avg. distance Rg = 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 Rr Boston* 88 155 6.8 5.7 30.8 84% 19% null 8.6 3.7 23.2 43% 16% model New 125 217 8.3 6.8 44.4 82% 15% York* null 11.7 4.0 33.5 34% 12% model LCM 184 194 62.8 20.6 86.2 33% 24% * from Youn, Gastner, Jeong, PRL (2008)
  21. 21. Navigator essentiality
  22. 22. 0 –2 –4 1 –6 –8 ln |e| –5 2 4 –6 3 –7 –8
  23. 23. 1 0 2 –5 3 –10 4 ln |e| –5 –6 –7
  24. 24. Optimizing spatial network for greedy navigators Fixed vertices, growing
  25. 25. Boston roads
  26. 26. MST
  27. 27. graph distance
  28. 28. Euclidean distance
  29. 29. Optimizing spatial network for greedy navigators Fixed vertices
  30. 30. Optimizing spatial network for greedy navigators Not fixed vertices
  31. 31. 0.2 BA deviation 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. 0.2 deviation 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 greedy navigators. Phys. Rev. Lett. 108:128701. SH Lee & P Holme, 2012. A greedy-navigator approach to navigable city plans. To appear in Eur. J. Phys. Spec. Top. SH Lee & P Holme, 2012. Geometric properties of graph layouts optimized for greedy navigation. Under review Phys. Rev. E.

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