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Nonetheless, these algorithms were developed with the objective of enumerating traces of big permutations which demand a huge processing time.
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The complexity of this algorithm is also exponential in a property of the traces called width (Braga, 2009), but, as the number of traces is usually much smaller than the number of solutions, enumerating traces runs considerably faster.
As a single trace can represent a big number of solutions, by enumerating traces we can generate a set much smaller than the complete set of solutions.
All proposed algorithms were able to enumerate traces for permutations with up to 200 elements.
When the number of enumerated traces decreases, the amount of space that we need to keep the traces in memory also diminishes.
For the non-deterministic algorithms, Figures 5 and 6 show also a gradual increment in the number of enumerated traces.
However, as the size of the permutations increases, the algorithm SWA outperforms the others with respect to the number of enumerated traces.
Figures 5 and 6 show that the increment of the execution time corresponds to a gradual increase in the number of enumerated traces.
To reduce memory consumption, we could print all enumerated traces but, as a result of this, we must add a post-processing step to eliminate the duplicate traces.
As it outputs the enumerated traces only when it reaches the last level, the necessary time limit to output at least one trace would be very close to the time required to enumerate all traces.
The three algorithms were designed to enumerate traces while a given execution time limit is not reached.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com