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- 1. Petter Holme Umeå University, Sungkyunkwan University, Stockholm University, Institute for Future Studies Sang Hoon Lee Umeå University, Oxford University
- 4. How can we measure navigability? What does optimally navigable networks look like?
- 6. 3 t 4 6 2 5 1 8 7 s 9
- 7. 3 t 4 6 2 5 1 8 7 s 9
- 8. 3 t 4 6 2 5 1 8 7 s 9
- 9. 3 t 4 6 2 5 1 8 7 s 9
- 10. 3 t 4 6 2 5 1 8 7 s 9
- 12. 3 t 4 6 2 5 1 8 7 s 9
- 13. 3 t 4 6 2 5 1 8 7 s 9
- 14. 3 t 4 6 2 5 1 8 7 s 9
- 15. 3 t 4 6 2 5 1 8 7 s 9
- 16. 3 t 4 6 2 5 1 8 7 s 9
- 17. 3 t 4 6 2 5 1 8 7 s 9
- 18. 3 t 4 6 2 5 1 8 7 s 9
- 19. (Greedy navigator) navigability Avg. distance Rg = Avg. distance for greedy navigators
- 20. (Greedy navigator) navigability Avg. distance Rg = Avg. distance for random navigators random navigators perform a random DFS
- 23. Rg = 33% Rr = 24%
- 24. 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)
- 26. 0 –2 –4 1 –6 –8 ln |e| –5 2 4 –6 3 –7 –8
- 27. 1 0 2 –5 3 –10 4 ln |e| –5 –6 –7
- 28. Optimizing spatial network for greedy navigators Fixed vertices, growing
- 29. Boston roads
- 30. MST
- 31. graph distance
- 33. Optimizing spatial network for greedy navigators Fixed vertices
- 37. Optimizing spatial network for greedy navigators Not ﬁxed vertices
- 40. 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
- 41. 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
- 42. 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.