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I think You can only justify not paying editors if your site is not for profit.
That would eliminate the backlog, but wouldn't cure the ill of not being able to process as much submissions as you get. There has to be a better way. With the popularity of submissions to directories specially the free ones, I'm sure many directories have the same problem. I thought a brainstorming might help. I have thought about this quite a bit.
IMO the ultimate solution would be some sort of an AI review. The decisions I make as a result of a review seem technically possible to be programmed into some code. For example semantics could be used to verify relevance to the submitted category and look for bad words. In any case I declare my backlog of a few months but people still choose to submit. I have put a lot of work into my directory and it gives me the blues when I see it has turned into a loosing battle.
We receive an average of 12,000 submissions per day. About 40% of them are eliminated by simply applying a filter to the submitted URL's. These are mostly easy to spot porn URL's.
We then "pre-crawl" the rest, eliminating nearly another 40% by applying a type of Bayesian filter.
What is left is cached and is human-reviewed, with several functions available to the editors which can wipe out hundreds of submissions in one swipe if a pattern is seen where someone is abusing the system. We try to only have to actually visit 1% of the sites submitted as what is usually reviewed is a cache of the web page.
This results in about 2,500 URL's being approved per day, which I believe is a pretty respectable number and would take a small army if not for the automated procedures.
One feature that has helped me(but not to the extent of eliminating the backlog) is the approval form is designed to easily browse through the directory and include in the appropriate category.
This is very important, but with us, most of our submissions are coming from submission services, so the webmasters often don't see our submission page. For example, we have a kids-only site which 90% of the submissions are for porn sites or non-English sites. Obviously the webmasters aren't seeing where they are submitting to.
You can put in word filters and domain filters, and use various methods to cut down on spam. But ultimately you might need to ask yourself if you are being over-ambitious. There are a lot of webmasters out there looking for listings, and many of them have good sites that are worth listing. If you don't have time to deal with them all, narrow your niche.
You can do this by excluding troublesome categories, or specifying a smaller region for your directory. You could make one part of the directory free, but all the other sections paid. Asking for money is easily the best way to stop most submitters in their tracks.
We found that by setting a decent add to price we get only quality businesses adding - which equals better quality links and higher satisfaction for our users...
If your directory is that popular shouldn't you be asking for paid inclusion?