Document Type

Conference Proceeding

Publication Date

8-1-2003

Publication Title

Computational Geometry: Theory and Applications

Abstract

We prove NP-hardness of a wide class of pushing-block puzzles similar to the classic Sokoban, generalizing several previous results [E.D. Demaine et al., in: Proc. 12th Canad. Conf. Comput. Geom., 2000, pp. 211-219; E.D. Demaine et al., Technical Report, January 2000; A. Dhagat, J. O'Rourke, in: Proc. 4th Canad. Conf. Comput. Geom., 1992, pp. 188-191; D. Dor, U. Zwick, Computational Geometry 13 (4) (1999) 215-228; J. O'Rourke, Technical Report, November 1999; G. Wilfong, Ann. Math. Artif. Intell. 3 (1991) 131-150]. 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.

Keywords

Combinatorial games, Computational complexity, Motion planning

Volume

26

Issue

1

First Page

21

Last Page

36

DOI

10.1016/S0925-7721(02)00170-0

ISSN

09257721

Rights

© the authors

Comments

Author submitted manuscript.

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