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Network Load Balancing in Logical Tree and Star Structures with Efficiency Metrics

This document explores the allocation and collection of tasks within logical tree and star network structures, focusing on efficient child allocation strategies. It discusses non-leaf child allocation and leaf child collection techniques, alongside various computational metrics such as solution time, computation, and latency. The analysis includes Gantt charts illustrating example networks with different node configurations and installment strategies, providing insights into the fraction of load given to nodes and the corresponding sizes of collected results.

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Network Load Balancing in Logical Tree and Star Structures with Efficiency Metrics

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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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