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But doing so will result in O |V|!) worst case running time.
The presented framework yields new worst case running time bounds for a family of important problems.
Therefore, Valiant's technique can be applied to reduce the worst case running times of a large family of important problems.
The algorithms presented in this paper improve the theoretical asymptotic worst case running time bounds for a large family of important problems.
Other consolidation algorithms, with linear worst case running time, have been devised by J. Kováč (personal communication) and K. Jahn (personal communication).
As in the worst case the algorithm can be executed Ω(n) times, the total worst case running time is O nC).
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To prove this the worst case run time is calculated in the following.
However, one of the fastest algorithms in practice has a worst case run time of O(n2).
The worst case run (even for ten boxes) was never above three minutes while the best case runs lasted around three seconds for two boxes and about 33 seconds in case of ten boxes.
Set D := D - C R. Since Algorithm 3 does not generate a distance matrix, its memory usage is only O(n) and the worst case run time is still O(n 2 l 2 ).
Even though the theoretical worst case run time of our algorithm increases exponentially with this parameter (which is to be expected due to the inherent computational complexity involved in computing a consensus of MUL-trees), for both examples presented above the run time was only a few seconds on a modern desktop computer.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com