How to limit link management to owner

I’m trying to set up a website where any user can register and add links. Ideally, he/she would also be able to manage those links, but I don’t want users to be able to modify or delete the links of others. As the Link Manager stands now, a user with the Manage Links capability can modify and delete the links of others.

I tried to set up a workaround using the Role Manager plugin such as the one created by Owen Winkler for editing others’ pages (here). I couldn’t get it to work, and I’m not sure if it’s possibile given the way that the Link Manager is set up.

Is this something that can be done easily? Or am I doomed to have to majorly hack the code to get this to work?