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This study delves into the problem of graph partitioning for cloud computing, focusing on communicating processes and bandwidth allocation among machines. Previous work in the field is discussed, along with related problems. The results showcase a good partition strategy utilizing disjoint covers with "good" sets, ensuring each vertex is covered adequately. The outline includes an introduction to the topic, details on the approach taken, and various covering methods for optimal graph partitioning. The study breaks down the challenges of min-max partitioning and emphasizes the ineffectiveness of any k-partition containing a specific vertex. The configuration, LP, and SSE approaches are also analyzed for effective partitioning. The study concludes with remarks on the effectiveness of different covering strategies in graph partitioning.
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. . . k 1 Motivation Cloud Computing n communicating processes Bandwidth B machines
Our Results Good Partition: Disjoint Cover with “good” sets (SSE’s)
Our Results Good Partition: Disjoint Cover with “good” sets (SSE’s) LP: Each vertex covered to extent 1
. . . k 1 Our Results Machines
Outline • Introduction • Graph Partitioning (quick intro) • Our Approach • Coverings to Partition
Graph Partitioning Approaches 0 1 (all vertices sit here)
Graph Partitioning Approaches 0 1 (all vertices sit here)
. . . 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)
Outline • Introduction • Graph Partitioning (quick intro) • Our Approach • Coverings to Partition
