Questions on the sorting/ordering functions of Mathematica (Sort, SortBy, Ordering, etc.).

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How to customize the order of leaf labels in a dendrogram plot?

Take the following simple case as an example: Needs["HierarchicalClustering`"] SeedRandom[99]; Sort@RandomInteger[99, {10}] gives {2, 7, 22, 34, 42, 58, 60, ...
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Finding correct combination of functions

I am trying to write code where I have an array $S$ or numbers in any order [5,4,2,1,....] Then I have a specific set of functions that I can write. ...
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Collision detection algorithm (discrete) with sweep and prune algorithm for periodic boundary conditions

EDIT: Question Updated with solution approach, but solution much slower than original implementation. Any ideas to speed up implementation? In the discussion on collision detection (see here) I asked ...
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How do I reassign canonical ordering of special expressions?

1. Default behavior of Sort Note: this peculiarity is described in a comment to a related question at StackOverflow but I think it's worth restating here at mma.sx. It is estabilished in ...