First off what is construction waste?
Answer Wood, Asphalt Shingles, Nails and Screws, Plaster, Drywall, Concrete, Rock, Ceramic Tile, Vinyl Flooring, Particle Board, Electrical Wire, Vinylsiding, Steel, Aluminum, Brass, Copper pipe, Steel pipe, Foam Insulation, Fiberglass Insulation, Stainless steel, Resellable Items, Ect.
All of these items are recyclable in some form.
Here is a breakdown on materials listed.
Asphalt shingles: These can be ground up reused for Hot Asphalt Mix, Cold Patch, Aggregate Road Base, and Fuel.
information links on asphalt shingle recycling
Plumbing parts: Plumbing parts and fixtures fall into three catagories
Metal: steel pipe, cast iron pipe and tubs, copper pipe, and brass valves and fixtures. SEE STEEL AND COPPER RECYCLING
Plastic: pvc pipe and plastic fixtures. SEE PLASTIC RECYCLING
Ceramic: sinks, toilets, urinals, and tiles.
Ceramics unfortunaly are difficult to recycle back to there original forms. However there are some efforts being made to crush these items and reuse them a aggrigate.
Wood: SEE WOOD RECYCLING