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Logical tree

P 0.0 E: 604 C: 103. P 0.0 E: 604 C: 103 L: 5. P 0.1 E: 707 C: 126. P 0.1 E: 707 C: 126 L: 2. Original physical grid. Logical network imposed on grid. Logical tree. Logical star. P 0.1.2 E: 415 C: 145. P 0.1.2 E: 415 C: 145 L: 3. Non-leaf.

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Logical tree

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  1. P 0.0 E: 604 C: 103 P 0.0 E: 604 C: 103 L: 5 P 0.1 E: 707 C: 126 P 0.1 E: 707 C: 126 L: 2 Original physical grid Logical network imposed on grid Logical tree Logical star P 0.1.2 E: 415 C: 145 P 0.1.2 E: 415 C: 145 L: 3 Non-leaf Child Allocation (Ci:parent*αi) Leaf Child Collection (δ*Ci:parent*αi) Solution time = 248.9 time units P 0 (Master: does not compute) P 0 (Master: does not compute) P 0 (Master: does not compute) Allocation (Ci*αi) Allocation (Ci*αi) Allocation (Ci*αi) Collection (δ*Ci*αi) Collection (δ*Ci*αi) Collection (δ*Ci*αi) Computation (Ei*αi) Computation (Ei*αi) Latency (Li) Latency (Li) Computation (Ei*αi) P 0.1 E: 461 C: 140 L: 5 P 0.2 E: 768 C: 125 L: 2 P 0.3 E: 678 C: 120 L: 1 P 0.4 E: 632 C: 139 L: 1 Note: αi = fraction of load given to node I, δ = size of collected result [0.0, 1.0] Note: αi = fraction of load given to node i, δ = size of collected result [0.0, 1.0] P 0.0 E: 599 C: 125 L: 1 Note: αi = fraction of load given to node I δ = size of collected result [0.0, 1.0] P 0.0.0 E: 568 C: 100 L: 9 P 0.0.0 E: 568 C: 100 P 0.0.1 E: 522 C: 105 L: 9 P 0.0.1 E: 522 C: 105 P 0.0.2 E: 795 C: 124 P 0.0.2 E: 795 C: 124 L: 6 P 0.1.0 E: 719 C: 103 P 0.1.0 E: 719 C: 103 L: 5 P 0.1.1 E: 566 C: 127 P 0.1.1 E: 566 C: 127 L: 3 Solution time = 216.4 time units Gantt chart of example star network with 5 processor nodes, δ = 0.5 Gantt chart of example 3-level tree network with 8 processor nodes, single-installment, δ = 0.5 Gantt chart of example 3-level tree network with 8 processor nodes (no latency), two-installment, δ = 0.5

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