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Min-Max Graph Partitioning

Min-Max Graph Partitioning. The Problem. k. 1. Motivation. Cloud Computing. n communicating processes. Bandwidth B. machines. Previous Work. A Related Problem. A Related Problem. Our Results. Our Results. Good Partition: Disjoint Cover with “good” sets (SSE’s). Our Results.

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Min-Max Graph Partitioning

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  1. Min-Max Graph Partitioning

  2. The Problem

  3. . . . k 1 Motivation Cloud Computing n communicating processes Bandwidth B machines

  4. Previous Work

  5. A Related Problem

  6. A Related Problem

  7. Our Results

  8. Our Results Good Partition: Disjoint Cover with “good” sets (SSE’s)

  9. Our Results Good Partition: Disjoint Cover with “good” sets (SSE’s) LP: Each vertex covered to extent 1

  10. Our Results

  11. . . . k 1 Our Results Machines

  12. Outline • Introduction • Graph Partitioning (quick intro) • Our Approach • Coverings to Partition

  13. Graph Partitioning Approaches 0 1 (all vertices sit here)

  14. Graph Partitioning Approaches 0 1 (all vertices sit here)

  15. . . . k 1 Breaks down for min-max 0 Any k-partitioning is bad: Part containing vertex 0 LP/SDP can always cheat (by smearing vertex 0) (even with triangle inequalities, all kinds of separating constraints)

  16. Outline • Introduction • Graph Partitioning (quick intro) • Our Approach • Coverings to Partition

  17. Configuration LP

  18. SSE

  19. Configuration LP

  20. Covering to Partition

  21. Covering to Partition

  22. Covering to Partition

  23. Covering to Partition

  24. Covering to Partition

  25. Covering to Partition

  26. Covering to Partition

  27. Covering to Partition

  28. Covering to Partition

  29. Covering to Partition

  30. Covering to Partition

  31. Concluding Remarks C B

  32. Thank you

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