To maximize the quantity of polymorphisms for a set number of marker M from an enter set of K markers, the next Integer Linear Programming formulation was described.
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Especially, if you're going to require the order about the keys, one example is if you would like be capable of record the keys in alphabetical order, then hash tables are no help (you'll need to type them), whereas you are able to straightforwardly traverse a lookup tree in order.
In the case of a compression purpose the domain would be the list of all finite size byte sequences and so will be the codomain. $endgroup$
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$begingroup$ To develop Patrick87's comment and help you better fully grasp the probabilistic counting algorithm : Linear Counting is utilized to get an approximate value of the volume of distinctive elements
$begingroup$ @MikeOunsworth equally I am able to wrap it these the output is truncated or padded If your msb can be a one. The output is now not of fixed duration, but is it nevertheless a hash perform? $endgroup$
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In the event the keys are strings (or integers), a trie might be an alternative choice. A trie can be a tree, but indexed differently from a search tree: you compose the key in binary, and go left for the 0 and suitable for the 1.
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If $L$ is larger than 1 ($L > one$), then surely (pigeonhole basic principle) some distinct names will be mapped on the same click here bit; but Nonetheless the amount of $1s$ in the final bitmask can nevertheless be utilized to approximate the amount of distinctive things in $S$;
