"Accountability Pal monitors your network and keeps track of who is using the Internet and what they are viewing, downloading, uploading, etc..."

Checking to see if Covenant Eyes worked on Ubuntu, I found Accountability Pal.

See http://www.accountabilitypal.org/about.php:

The Problem

These days, more men and women are becoming addicted to viewing pornography on the Internet. Web sites offer free glimpses into enticing worlds of sexual immorality, and the anonymity that the Internet has to offer provides a way of indulging in those desires in the privacy of your own home without the worry of getting caught by their spouse or other loved ones. As a result, when the addiction is discovered by someone else, it often has such a devastating effect that families are destroyed as a result.

The Solution

Accountability Pal monitors your network and keeps track of who is using the Internet and what they are viewing, downloading, uploading, etc. It emails a report (in PDF format) of each user's activity to the person/people you specify. I originally wrote Accountability Pal to allow people with addictions to porn sites to become accountability partners. There are commercial services that do this, but they usually charge a monthly fee of $10 or more.

The other accountability tools out there, run on the PC's being "watched" and can be easily circumvented by the user. Accountability Pal is designed to be run on a Linux server where users can't simply disable the software running on their PC. A Windows version is on the way as well that will be designed to be more secure than just an application running as an icon on the task bar.
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Read more: http://www.accountabilitypal.org/about.php.