See following image. Who is Run-out?
A is crossed the crease and B is crossed half of the pitch. Run-out happening in B's side. Then who is out? A or B?
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B is out. The batsmen haven't crossed each other and B is closer to the end where the fielder puts the wicket down.
From the wikipedia Page
The batsman can be judged run out when he is closest to the end where the wicket has been put down by the opposition and no other batsman is available inside the crease of the same end.
Another Reference.Check the 3rd Point
It is not a question of which batsman has covered the greater proportion of the pitch, but rather it is a question of whose is the ground where the wicket is put down.
Law 38.3 Which batsman is out
The batsman out [...] is the one whose ground is at the end where the wicket is put down.
Law 29.2 Which is a batsman’s ground
(c) If there is no batsman in either ground, then each ground belongs to whichever batsman is nearer to it, or, if the batsmen are level, to whichever batsman was nearer to it immediately prior to their drawing level.
In this case, B's is the ground where the wicket b has been put down. Therefore B will be out.