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

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: . t. S. Low Color Partitions. Decomposition of a graph into several components (disjoint). Properties of this partition: The components have bounded diameter Coloring:

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

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  1. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.:

  2. t S

  3. Low Color Partitions • Decomposition of a graph into several components (disjoint). • Properties of this partition: • The components have bounded diameter Coloring: • Components that are “close” to each other cannot have the same color. Parameter • Color the partition (at each level) with minimal # of colors.

  4. Why Low-Color Partitions? • Clusters of same color are far away from each other. • Leaders of these clusters are mutually far off. • The real data sources that feed those leaders will also be mutually far away. • The number of such real data sources that are mutually far away are significant (compared to those that are closeby).

  5. Benefit of Low-Color Partitions Cluster Leader

  6. Benefit of Low-Color Partitions Data Sources

  7. Benefit of Low-Color Partitions

  8. Benefit of Low-Color Partitions

  9. Benefit of Low-Color Partitions Higher Level Leader

  10. Path Separators • A set of shortest paths that partition a graph into two or more components of size atmost n/2 (n is total size of the graph). • Path Separators can be computed in polynomial time • Planar Graphs are 3-path separable • H-Minor Free Graphs are k-path separable

  11. Graph Decomposition (Planar Graph)

  12. Graph Decomposition Level 1 Cluster

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