Brewing and composting are basically the same process, the difference being composting is less defined and the output is, well, less tasty.
Composting is essentially the breakdown of organic material by microbes, which is what brewing is. I have a compost pile, which loves my brewing leftovers. My understanding is the bin works better under more ideal cicumstances. Actually, my pile does too, but I care less, it will break down eventually, bins are designed to speed up the process.
From what I have read, brewing waste has a slightly low pH (acidic). There is also a balance of carbon to nitrogen that creates an ideal compost. Brewing waste is high in carbon. Adding a little lime (or fertilizer, which seems silly) should speed up the process. There are other sources high in nitrogen you can add, green grass clippings being one. Your bin probably came with a "recipe" for ideal compost.
The last thing you want to do is throw away, or flush your brewing waste. MIcrobreweries are on the cutting edge of going green, homebrewers should follow suit.