Run shell / batch file on new post or edits

I’d like to be able to run a Linux shell / batch file on posting a new page, the idea being to update a headline-include file created via simplepie rather than the “run a chron job for updates every 15 minutes even though we only have two or three posts a day” method.

I can run the file manually but in a shared environment it would be far better if it was automatic. Surely there’s an easy way to do this?