... | ... | @@ -24,7 +24,9 @@ LinkTest can also group processes according to their hostname. In this case test |
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Differs from the previous in that the even number of groups is split into bisecting halves and only the connections between the two halves are tested. Note that the possible permutation space exhibits a similar behavior as to the full test, i.e. for large $`n`$ it becomes neigh impossible to iterate through all possible combinations.
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## Comparison
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![GroupByHostComparison.svg](uploads/26367c81579ccab257309afe4691d91e/GroupByHostComparison.svg)
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The above figure compares the communication patterns for 16 processes split into four groups with a common hostname (red, green, blue and magenta) a possible 1-Factor communication scheme. The colored lines between the rounded boxes with numbers, which denote the group-local process number, a tested connection between two process. The color of the line indicates the step in which the connection was tested. Lines with a common color correspond to connections that are tested together in the same step. In the 1-Factor diagram we find connections between all possible nodes. In the hostname-grouping diagram we only find connections between the four differently colored groups. In a given step all processes from one group only communicate with the processes of one other group. In the bisection diagram we only find connections between the upper-left and lower-right set of hosts. The dashed line denotes the bisection split of the processes. The hostname bisection diagram is a combination of the hostname grouping and bisection. Like the bisection diagram communication only occurs across the dashed diagonal, but now in any step all processes from a given group only communicate with the processes of one other group.
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## Derivation: Number of Permutations
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... | ... | @@ -79,8 +81,4 @@ P=\prod\limits_{j=0}^{n-2}\prod\limits_{i=0}^{n/2-1}\bigg[\begin{pmatrix}n-2i\\2 |
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In the limit as $`n`$ tends to infinity $`P`$ tends towards:
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```math
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\lim\limits_{n\to\infty}P=(n!)^n
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```
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```math
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\Delta = \nabla^2 = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2}
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``` |
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\ No newline at end of file |