Here is the puzzle:
(Click on the image to see a larger image.)
This is a word graph. The nodes are short words, the edges are long words.
Whenever an edge (i.e., a long word) connects two nodes (i.e., two short words) it means that the long word can be reversed and decomposed into the two short words. Another way to say it: The two short words can be reversed and interleaved in some way to produce the long word.
Fill in each of the numbered nodes (1-18) with the appropriate short word. Optionally, label each of the edges with the appropriate long word. (Although it's not much of an option because everything is interdependent, so you will have to figure most of them out anyway.)
The grayed-out nodes and edges are also part of the graph. They are additional connections provided to assist you by giving you more information.
For illustrations of the connecting mechanism, you can look at the shaft of the arrow which is already complete. Let's look at how BONELESS connects SLOB and SEEN:
Start with the two short words: SLOB SEEN Reverse them: BOLS NEES Interleave them (you can space the letters out however you wish, but you must maintain their order): BOLS NEES BO L S NE E S BONELESS
Obviously, you can reverse the process to decompose BONELESS into SLOB and SEEN.
Consider this puzzle to have a partial NO-COMPUTERS tag attached. You may write computer programs or use existing tools for pattern matching or regular expressions in order to find short word and long word candidates. However, you may not write a computer program to solve the entire puzzle brute force.
In your answer, please briefly indicate your methods.
You will be doing a lot of thinking in reverse for this puzzle. I would advise you to mark your current position in space-time so that you can find your way back afterward.
A few notes about @DrXorile 's solution:
Node #3 is EMIT (+NOON = NOONTIME, +NAPS = TIMESPAN, +TRAP = PARTTIME)
Node #10 can be RUT or TANG or even TIDE again
Node #18 really is DECOR