E. Demaine, M. L. Demaine and J. O'Rourke [2000], PushPush and Push-1 are NP-hard in 2D, Proc. 12th Annual Canadian Conf. on Computational Geometry , Fredericton, New Brunswick, Canada, pp. 17-20.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of Sliding Block Puzzles The time complexity of sliding block puzzles was the subject of intense research in the past. Though seemingly trivial, most variations are at least NPhard and, some, even PSPACE complete. Table 2 shows some results. The table was basically taken from Demaine et al. [DDO00], extended by the category of games where the blocks are pushed by an external agent not represented on the board, into which Atomix falls. The columns mean: 1. Are the moves performed by a robot on the board, or by an outside agent 2. Can the robot pull as well as push 3. Does each block ....

....di#erence does not a#ect the time complexity significantly. 5 1. 2. 3. 4. 5. 6. 7. 8. 9. Game Robot Pull Blocks Fixed # Path Slide Dim. Complexity L k 2D NP hard [Wil88] unit k 2D NP hard [DO92] PushPush3D 1 3D NP hard [OT99] PushPush 1 2D NP hard [DDO00] k 2D open [DO92] 2D NP hard [OT99] Push # k 2D NP hard [Hof00] Sokoban 12 2 2D PSPACE compl. DZ99] 15 Puzzle 2D NP hard [RW90] Rush Hour 1 2,3 1 2D PSPACE compl. FB02] 2D PSPACE compl. HS01] Table 2: Time complexity ....

Erik D. Demaine, Martin L. Demaine, and Joseph O'Rourke. PushPush and Push-1 are NPhard in 2D. In Proceedings of the 12th Canadian Conference on Computational Geometry, pages 211--219, Fredericton, New Brunswick, Canada, August16--18 2000.

....the board to form the given molecule Obviously, this problem can be formalized as a state space search problem, which recently was undertaken by H u ner et al. 9] There di erent heuristic search methods were presented. Atomix falls into the category of sliding block puzzles as, e.g. PushPush [3], Sokoban [2, 4] or 15Puzzle [12] where time and space complexity was, and still is, subject of intense research. Though seemingly trivial, most variations are at least NP hard, and contained in PSPACE; some are even PSPACE complete we refer the reader to, e.g. Balc azar et al. 1] for further ....

....game levels. Finally we summarize some complexity results on block sliding puzzles, into which Atomix falls. As already mentioned in the introduction most of these problems are NP hard and contained in PSPACE; some of them are even PSPACEcomplete. The following table is taken from Demaine et al. [3], extended by the category of games where blocks are pushed by an external agent not presented on the board. The columns mean: 1. Are the moves done by a robot on the board, or by an outside agent 2. Can the robot pull as well as push 3. Are all block unit squares, or may the have di erent ....

[Article contains additional citation context not shown here]

E. D. Demaine, M. L. Demaine, and J. O'Rourke. PushPush and Push-1 are NP-hard in 2D. In Proceedings of the 12th Annual Canadian Conference on Computational Geometry, pages 17-20, Fredericton, New Brunswick, Canada, August 2000.

....Puzzles The time complexity of sliding block puzzles was the subject of intense research in the past. Though seemingly trivial, most variations are at least NP hard and, some, even PSPACE complete. The following table shows some results. The table was basically taken from Demaine et al. [3], extended by the category of games where the blocks are pushed by an external agent not represented on the board, into which Atomix falls. The columns mean: 1. Are the moves performed by a robot on the board, or by an outside agent 2. Can the robot pull as well as push 3. Does each block ....

E. D. Demaine, M. L. Demaine, and J. O'Rourke. PushPush and Push-1 are NPhard in 2D. In Proc. 12th Canadian Conf. Computational Geometry, pp. 211219, Fredericton, 2000.

....Puzzles The time complexity of sliding block puzzles was the subject of intense research in the past. Though seemingly trivial, most variations are at least NP hard and, some, even PSPACE complete. The following table shows some results. The table was basically taken from Demaine et al. [3], extended by the category of games where the blocks are pushed by an external agent not represented on the board, into whichAtomix falls. The columns mean: 1. Are the moves performed by a robot on the board, or by an outside agent 2. Can the robot pull as well as push 3. Does each block ....

E. D. Demaine, M. L. Demaine, and J. O'Rourke. PushPush and Push-1 are NPhard in 2D. In ##### #### ######## ##### ############# ########, pp. 211219, Fredericton, 2000.

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Erik D. Demaine, Martin L. Demaine, and Joseph O'Rourke. PushPush and Push-1 are NP-hard in 2D. In Proceedings of the 12th Annual Canadian Conference on Computational Geometry, pages 211--219, Fredericton, Canada, August 2000. http://www.cs.unb.ca/conf/ cccg/eProceedings/26.ps.gz.

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E. D. Demaine, M. L. Demaine, and J. O'Rourke. PushPush and Push-1 are NPhard in 2D. In Proc. 12th Canadian Conf. Comput. Geom., pp. 211-219, 2000. http://www.cs.unb.ca/conf/cccg/eProceedings/26.ps.gz.

....Blocks is NP Complete for Noncrossing Solution Paths Erik D. Demaine Michael Ho mann y Abstract We prove NP hardness of a wide class of pushing block puzzles like the classic Sokoban, generalizing several previous results [4, 5, 7, 8, 13, 15]. 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 speci ed goal position. In the Push k puzzle, the robot can push up to k blocks in front of it as long as there is at least one free square ....

....A robot can move horizontally and vertically in the grid, and thereby push up to k blocks in front of it, for some constant k. See Figure 1, in which the blocked positions are shaded and the robot is shown as circle, pushing two blocks. Figure 1: Example of pushing blocks. The Push k problem [4, 5] is to decide whether there is a sequence of moves starting at a speci ed free position and ending at a speci ed goal position. If we omit the restriction on how many blocks the robot can push at once (i.e. k = 1) we obtain the problem Push [2, 6, 7, 12] To make these basic problems more ....

[Article contains additional citation context not shown here]

Demaine, E. D., Demaine, M. L., and O'Rourke, J. PushPush and Push-1 are NP-hard in 2D. In Proc. 12th Canad. Conf. Comput. Geom. (2000), pp. 211{ 219.

....Blocks is NP Complete for Noncrossing Solution Paths Erik D. Demaine Michael Ho mann y Abstract We prove NP hardness of a wide class of pushing block puzzles like the classic Sokoban, generalizing several previous results [3, 4, 6, 7, 12, 14]. 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 speci ed goal position. In the Push k puzzle, the robot can push up to k blocks in front of it as long as there is at least one free square ....

....Zurich, Switzerland, hoffmann inf.ethz.ch. in the grid, and thereby push up to k blocks in front of it, for some constant k. See Figure 1, in which the blocked positions are shaded and the robot is shown as circle, pushing two blocks. Figure 1: Example of pushing blocks. The Push k problem [3, 4] is to decide whether there is a sequence of moves starting at a speci ed free position and ending at a speci ed goal position. If we omit the restriction on how many blocks the robot can push at once (i.e. k = 1) we obtain the problem Push [1, 5, 6, 11] To make these basic problems more ....

[Article contains additional citation context not shown here]

Demaine, E. D., Demaine, M. L., and O'Rourke, J. PushPush and Push-1 are NP-hard in 2D. In Proc. 12th Canad. Conf. Comput. Geom. (2000), pp. 211{ 219.

No context found.

E. Demaine, M. L. Demaine and J. O'Rourke [2000], PushPush and Push-1 are NP-hard in 2D, Proc. 12th Annual Canadian Conf. on Computational Geometry , Fredericton, New Brunswick, Canada, pp. 17-20.

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