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Tight Bounds for Online Vector Bin Packing

Tight Bounds for Online Vector Bin Packing. Ilan Cohen Joint work with : Yossi Azar ,Bruce Shepherd, Seny Kamara. Jobs Scheduling. Scheduler. Server N. Server 1. Jobs Scheduling. Server. CPU. Memory. GPU. …. Cloud Computing. Vector Bin Packing. On Line Algorithms.

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Tight Bounds for Online Vector Bin Packing

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  1. Tight Bounds for Online Vector Bin Packing

    Ilan Cohen Joint work with: YossiAzar ,Bruce Shepherd, SenyKamara
  2. Jobs Scheduling Scheduler Server N Server 1
  3. Jobs Scheduling Server CPU Memory GPU …
  4. Cloud Computing
  5. Vector Bin Packing
  6. On Line Algorithms
  7. Competitive Ratio
  8. Related Results
  9. Our Results
  10. Vector Bin Packing
  11. Our Results
  12. VBP(B=1) Lower Bound Online- VBP (B=1) α bins. Online- Graph coloring α colors
  13. On-line Graph Coloring e c a a b b c d d e
  14. On-line Graph Coloring
  15. VBP(B=1) Lower Bound Online- VBP(B=1) α bins Online- Graph coloring α colors
  16. Reduction VBP to Graph Coloring
  17. Reduction VBP to Graph Coloring Vec: Ind:
  18. Reduction VBP to Graph Coloring a b c d e a b c d e
  19. Reduction VBP to Graph Coloring Vec: Ind:
  20. Reduction VBP to Graph Coloring a a b b c c d d
  21. VBP(B=1) Lower Bound Online- VBP(B=1) α bins Online- Graph coloring α colors
  22. VBP(B=2) Lower Bound k colors for each sub graph Online VBP(B=2) α bins α classes of Triangle-free sub graphs Online- Graph coloring α·k colors
  23. Reduction VBP to Graph Coloring
  24. Reduction VBP(B=2) to Graph Coloring
  25. Reduction VBP(B=2) to Graph Coloring d c a b
  26. Reduction VBP(B=2) to Graph Coloring
  27. VBP(B=2) Lower Bound Online VBP(B=2) α bins α classes of Triangle-free sub graphs Online- Graph coloring α·k colors
  28. Reduction VBP(B=2) to Graph Coloring
  29. On-line Graph Coloring
  30. On-line Graph Coloring
  31. VBP(B=2) Lower Bound Online VBP(B=2) α bins α classes of Triangle-free sub graphs Online- Graph coloring α·k colors
  32. Coloring vertices of bin j a b c d
  33. Correctness
  34. Analysis
  35. VBP Lower Bound Online- Graph coloring α· colors Online VBP (B) α bins α·k classes of B clique free graphs α classes of B+1 clique free graphs
  36. B Clique Free to B-1 Clique Free
  37. Reduction VBP to Graph Coloring
  38. Reduction VBP to Graph Coloring
  39. Scheme
  40. Analysis
  41. Upper Bound (B > 1)
  42. Pack Into Virtual bins All Vector Stream: cBlog(d) B OPT virtual bins
  43. Distribute bin vectors Virtual Bin i: cBlog(d) B B r bins B B
  44. The virtual VBP algorithm.
  45. The virtual VBP algorithm.
  46. Proof Sketch
  47. Distribute bin vectors Virtual Bin i: cBlog(d) B B r bins B B
  48. Distributing the vectors
  49. Distributing the vectors
  50. De-randomize the algorithm
  51. De-randomize the algorithm
  52. De-randomize the algorithm
  53. Conclusions
  54. Open Questions
  55. Thank you!
  56. The {0,1}-VBP Upper Bound
  57. The {0,1}-VBP Upper Bound
  58. Unrelated Machine Model
  59. Unrelated Machine Model
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