Water softener drain connect to kitchen sink?

I currently have a Portable Exchange service for my water softener. I'm tired of the monthly bill and the monthly visit to replace the tank, so I'm looking at replacing it with a more conventional water softener. The nearest and best place to drain the new softener is my kitchen sink. It's your standard p-trap, pvc, dual stainless sink setup. My question: How do I best make this connection from the softener's 1/2" ID drain pipe to the pvc under the sink? What is the best practice? I have very little room to work with here. Is there some sort of pvc pipe fitting that has a provision to connect the softener line? Thanks for your help!

I would figure some thing else out...
Maybe figure out how to use the laundry drain.

Oh, I would love to be able to do that. The problem is that I don't have much to work with. The house is very small and on a slab. Everything is in the kitchen. Water softener and sink are on one side of the galley kitchen and on the opposite side is furnace, water heater, and washer/dryer. To get the drain line over to that other side I'd have to go through the concrete slab or up the wall and over the ceiling. Neither are very appealing to me...

It has to be indirect wasted into a vented trap.

Up and over and then put it in the corner of the wall and Ceiling and then cover with triming... or make a channel over it if there is no corner for it to go into..