Filter question about combating algae

Hello all, I have been having a moderate reoccurance with algae this past month. I was told by my LPS to never vacume green algae, but being a "green" pool owner, I did. Now I am going through the process of brushing and shocking. My question is should I run the filter now, or do I wait until the algacide kills the algae first? My LPS told me when the green becomes gray, the algae is dead. Thanks!
Rich
 
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