1. [email_address]

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Computer Science

Web-

Highway dimenstion

NPvs P

4. 5. 6. 7. 8. 9. 10. 11. + 12. Computer Science , P= A = M - R 2 M - M ( i , j )R 2 i j 13. 14. 15. + = PROFIT + 16. - 17. - 18. -

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Barabashi, Albert, 1999, 2000

5 ,

- :

• kkt , k 1

{5, 6}

• P(d)c / d

• 2.1, c

19. - - , 20. - G(n,p) V = {1, 2, , n}, E - p[0, 1] e 1 , , e m , m = C 2 n < n , F n , P n,p > n= {G = (V n , E)} F n =2 n P n,p (G) = p |E| (1-p) m-|E|- 21. 22. Highway dimension 23. Highway dimension

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A*

24. P vs NP 25. 1 ! 26. 27. P vs NP C, I S ,I . S C(S, I) = true NP , P , P NP , , , AB 28. 29. 30. .. 31. I think it wise, and only honest, to warn you that my goal is immodest. It is not my purpose to "transfer knowledge" to you that, subsequently, you can forget again. My purpose is no less than to effectuate in each of you a noticeable, irreversable change. I want you to see and absorb calculational arguments so effective that you will never be able to forget that exposure. I want you to gain, for the rest of your lives, the insight that beautiful proofs are not "found" by trial and error but are the result of a consciously applied design discipline. I want to inspire you to raise your quality standards. I mean, if 10 years from now, when you are doing something quick and dirty, you suddenly visualize that I am looking over your shoulders and say to yourself "Dijkstra would not have liked this.", well, that would be enough immortality for me.