Paper by Martin L. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, and Joseph O'Rourke, “PushPush is NP-hard in 2D”, Technical Report 065, Smith College, January 2000.

Abstract:

We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. 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, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 2D by reduction from SAT.

Comments:

This paper is also available as arXiv:cs.CG/0001019 of the Computing Research Repository (CoRR).

Length:

The paper is 18 pages.

Availability:

The paper is available in PostScript (719k) and gzipped PostScript (179k).

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Related papers:

CCCG2000b (PushPush and Push-1 are NP-hard in 2D)

Related webpages:

PushPush (Erik Demaine)
Pushing Blocks (Erik Demaine)