The league's "important dates" page says the conference finals will begin on May 20 (if that's Game 1 of whichever series starts first, the second series would then start on the 21st), with a possible move-up to May 18 or 19. So, basically, for the teams that get there, the conference finals will start no earlier than the 18th and no later than the 21st.
Since ESPN/ABC has the East Finals this year, it seems likely that the plan is for the East Finals to start in the 18th (Sunday) if possible. That should put the West Finals starting no earlier than the 19th, but that's just a guess.

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I've got more to go on than I did before.
