Paper by Erik D. Demaine

Erik D. Demaine, Martin L. Demaine, Michael Hoffmann, and Joseph O'Rourke, “Pushing Blocks is Hard”, Computational Geometry: Theory and Applications, volume 26, number 1, August 2003, pages 21–36. Special issue of selected papers from the 13th Canadian Conference on Computational Geometry, 2001.

We prove NP-hardness of a wide class of pushing-block puzzles similar to the classic Sokoban, generalizing several previous results [5,6,9,10,15,17]. The puzzles consist of unit square blocks on an integer lattice; all blocks are movable. The robot may move horizontally and vertically in order to reach a specified goal position. The puzzle variants differ in the number of blocks that the robot can push at once, ranging from at most one (PUSH-1) up to arbitrarily many (PUSH-*). Other variations were introduced to make puzzles more tractable, in which blocks must slide their maximal extent when pushed (PUSHPUSH), and in which the robot's path must not revisit itself (PUSH-X). We prove that all of these puzzles are NP-hard.

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The paper is 19 pages.

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Related papers:
PushXCCCG2001 (Pushing Blocks is NP-Complete for Noncrossing Solution Paths)

Related webpages:
Pushing Blocks

See also other papers by Erik Demaine.
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Last updated May 28, 2024 by Erik Demaine.