PushPush and Push-1 are NP-hard in 2D

Abstract

We prove that two pushing-blocks 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 Push-1. 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 Push-1 version, the agent can only push one block one square at a time, the minimal extent|one square. Both NP-hardness proofs are by reduction from SAT, and rely on a common construction .

Extracted Key Phrases

1 Figure or Table

Showing 1-8 of 8 references

Push-is NP-hard

  • M Hof, Hoomann
  • 2000

PushPush is NP-hard in 2D Paper cs.CG/0001019, arXiv.org e-print archive

  • Ddo, E D Demaine, M L Demaine, J O 'rourke
  • 2000

Paper cs.CG/9911013, arXiv.org e-print archive

  • Ma
  • 1999

Sokoban is PSPACE-complete

  • J Cul, Culberson
  • 1998

Rourke and the Smith Problem Solving Group. PushPush is NP-hard in 3D

  • Os J
Showing 1-10 of 28 extracted citations

Statistics

051015'02'04'06'08'10'12'14'16
Citations per Year

59 Citations

Semantic Scholar estimates that this publication has received between 30 and 117 citations based on the available data.

See our FAQ for additional information.