All the above information is good and scientific and helpful and should work. Here's a method that I have used that has a lot of other benefits that I will explain.
As mentioned above this red slime algae (if you will excuse my lack of scientific naming - I"m an aquarist, not a biologist) is a healthy addition to your aquarium (and to general air quality and ozone and all that). Erradication of it is not a healthy solution. Control of it is what is desired. We don't want it coating everything in the tank and killing stuff and looking like a fish tank from hell rather than a small piece of paradise behind glass (or acrylic in my case).
The last thing that you want to do is to put in some kind of chemical to kill the stuff - NOT GOOD - The light method is good for a FO tank; In a reef aquarium there are things like anemones, various corals, and algaes that depend on light quality and duration to survive adequately. Of course some people do have a tendancy to leave lights on too long (timers are the key... you select the exact amount of time... don't try to remember to turn them on and off.... that's never gonna work). I would suggest that 11 hours of full light a day is just about right for a healthy reef.
OK, now that that's out of the way here is my solution. Part 1: Nassarius obsoletus snails - and a lot of em! I have an 85 gallon reef and I have 200 of these guys in there! They're awesome! during the majority of the day they are buried under the sand out of site (good for those of you who don't think snails are attractive). at night they come out of the sand and clean the glass for you (which is pretty cool in my opinion, although sometimes they miss a spot or two... guess they can't see the big picture like me
) They also will come crawling out of the sand every time you feed your fish and do an excellent job of eating any excess food that falls on the substrate and eating detritis in general. This helps your water quality in a huge way!
Part 2: Astrea snails! I have about 40 in my tank. These guys are great because they're a bit more attractive and they are hard workers (sometimes they will have macro algaes growing on their shells... kinda cool!) They tend to clean all the places where the other guys miss eg: LR! The will keep you LR slime free (almost)! When I had a problem with slime I would hand place these guys smack dab in the middle of the problem patches and let em go at it! They'de desimate the red slime on a medium rock in one day.
Part 3: about 20 little tiny hermits (never get big ones!!! Huge problems!) these guys not only keep the slime down, but they also graze on the hair algea as well.
Basically this solution is to keep critters in your tank that eath the algae which allows the algae to grow and benefit your tank without taking over your tank. Also the snails that burrow into your sand will help keep the substrate clean simply by moving it and thus slowing the spread of slime algaes.
The bio diversity of this method is very beneficial to reef tanks! just be careful that you don't mix things that kill eachother and things that you are trying to keep alive!