Best linux backup software that is most like Time Machine

Question

What is the best Linux Mint backup tool that is most like Time Machine (that ships on Macs)?

The one thing that I want it to have similar to Time Machine is that it only backs up files that have been changed, therefore making for faster backups.

Solution

Incremental backup has been a feature of operating systems for essentially ever. If by Mac-like, you mean GUI heavy, these look like decent contenders:

https://backintime.readthedocs.io/en/latest/
http://sourceforge.net/projects/sbackup/

I use command line tools so can't recommend either.

Update: I installed backintime on my Ubuntu Lucid system for testing. It seems competent and complete although its space requirements are relatively high as the backups aren't bundled, compressed, nor encryptped. This makes for really rapid restoration, and disk space is pretty cheap but I wouldn't use it for full system backups.

However, for home directory backups it is pretty well suited which makes its "every 5 minute" schedule option reasonable. Out of the box it just does the right thing with minimal configuration. As with many user-oriented tools, it trades utility for dirt simplicity.

It is available on the Ubuntu (therefore Mint) repositories as backintime-gnome or backintime-kde.