As for most languages, the french language practice obeys some rules. One of these rules is called "règle de l'article contracté". It states that when "une préposition" is followed by "un article défini", the result should be "un article contracté" (contracted article).
In the case of:
une compression du personnel
"du" is here the contracted article of "de le" which respectively are "préposition + article défini". Consequently, it is incorrect to say:
une compression de le personnel
The use of "de" / "du" depends on whether "personnel" is definite or not. In our case, it isn't so one must use "du".
If "personnel" is definite, "de" should be used as in:
une compression de personnel de la comptabilité.
Note that "de la" of "de la comptabilité" is not concerned by the rule in question since it is "du genre féminin" (feminine gender).
