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Bi-criteria Linear-time Approximations for Generalized k-Mean/Median/Center

Bi-criteria Linear-time Approximations for Generalized k-Mean/Median/Center. Speaker: Dan Feldman Joint work with Amos Fiat, Danny Segev & Micha Sharir. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A A A A A A A A. 1-Line Median.

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Bi-criteria Linear-time Approximations for Generalized k-Mean/Median/Center

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  1. Bi-criteria Linear-time Approximations for Generalized k-Mean/Median/Center Speaker: Dan Feldman Joint work with Amos Fiat, Danny Segev & Micha Sharir TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAAAAAA

  2. 1-Line Median

  3. 1-Line Median

  4. -Line Median

  5. -Approximation (PTAS)

  6. -Line Mean -Line Median -Line Center

  7. -Line Median/Mean/Center is NP-Hard

  8. (a,)-Approximation and and

  9. Example: The 2-Line Median of P

  10. (3,½)- approximation to the2-Line Median of P

  11. (4, 10)- approximation to the2-Line Median of P

  12. k j-Flat Median/Mean/Center A set F of k j-dimensional flats that minimizes the sum of distances/ sum of squared distances/ maximum distance from P to F

  13. Results for

  14. Results for

  15. Results for

  16. Our Result

  17. Applications for

  18. Applications for

  19. The Algorithm

  20. Input TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA

  21. Output (with high probability)

  22. Output (with high probability)

  23. Initialization  

  24. Proof of Correctnessfor the case of lines ( j=1)

  25. Main Technical Theorem

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