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Theoretical running times are polynomial in all factors except d.
The worst theoretical running time of the algorithm for calculating the quartet distance presented above is O(n).
These theoretical running times have been validated by running a series of tests using a Java implementation of the algorithm, available at [ 15].
In addition to the above discussion of theoretical running times of different methods, we measure empirical running times for NetDis and GCD.
We have no theoretical running time for this data, but the graphs show that the running time is O(n).
This also allows for heuristics that reduce the theoretical running time to O( <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0009490.e006.PNG" class= inline-graphic"/> ).
Similar(53)
But this theoretical neatness runs into a practical problem.
The theoretical minimum run time, as simulated using the genie-aided bound function, leads to additional reductions of 66.3% (N = 40) and 57.7% (N = 80).
These new (and in some cases theoretical) plans run counter to narratives about US departure from the region.
Hutchinson and Garcia [68] used Fr = 16 to estimate theoretical, highest-speed running in Tyrannosaurus (although they regarded such a speed as unlikely), and thus we apply that assumption here as well.
In practice, we find that RAF's scaling reflects the theoretical bounds, achieving running times often an order of magnitude faster than current simultaneous alignment and folding methods.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com