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Several variants of A* have been recently proposed for find-ing optimal solutions for the multi-agent pathfinding (MAPF)problem. However, these variants have not been deeply com-pared either quantitatively or qualitatively. In this paper weaim to fill this gap. In addition to obtaining a deeper under-standing of the existing algorithms, we describe in detail theapplication of the new enhanced partial-expansion techniqueto MAPF and show how pattern databases can be applied ontop of this technique.