PushPush and Push1 are NPhard in 2D
Abstract
We prove that two pushingblocks puzzles are intractable in 2D. One of our constructions improves an earlier result that established intractability in 3D [OS99] for a puzzle inspired by the game PushPush. The second construction answers a question we raised in [DDO00] for a variant we call Push1. Both puzzles consist of unit square blocks on an integer lattice; all blocks are movable. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover when a block is pushed it slides the maximal extent of its free range. In the Push1 version, the agent can only push one block one square at a time, the minimal extentone square. Both NPhardness proofs are by reduction from SAT, and rely on a common construction.
 Publication:

arXiv eprints
 Pub Date:
 July 2000
 arXiv:
 arXiv:cs/0007021
 Bibcode:
 2000cs........7021D
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics;
 F.2.2
 EPrint:
 10 pages, 11 figures. Corrects an error in the conference version: Proc. of the 12th Canadian Conference on Computational Geometry, August 2000, pp. 211219