M. Holzer and S. Schwoon. Assembling molecules in Atomix is hard. Theoret. Comput. Sci., 303(3):447--462, 2004. 15 Home/Search Document Details and Download
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Finding Optimal Solutions to Atomix - Hüffner (2002) (Correct)
.... 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 of some sliding block puzzles. Our implementation handles di#erent possible goal positions by imposing a move limit and trying all possible goal positions with that limit, and repeating with an incremented move limit until a solution is found. There are also some ....
....that Sokoban, which shows some similarities to Atomix, is PSPACE complete, it doesn t seem unlikely that Atomix falls into this class, too. This would imply the existence of superpolynomially long optimal solutions (unless NP = PSPACE) After submission of this paper, Holzer and Schwoon [HS01] showed by reduction from nonempty intersection of finite automata that Atomix is indeed PSPACE complete. They also provided a level with an exponentially long optimal solution. 5 Searching the State Space of Much progress has been made in the area of heuristic search. This is due to three ....
Markus Holzer and Stefan Schwoon. Assembling molecules in Atomix is hard. Technical Report TUM-I0101, Institut fur Informatik, Technische Universitat Munchen, May 2001.
Finding Optimal Solutions to Atomix - Hüffner, Edelkamp, Fernau.. (2001) (Correct)
....Complexity PushPush3D unit 1 3D NP hard PushPush unit 1 2D NP hard Push unit k 2D NP hard Sokoban 1 2 2 2D PSPACE compl. Sokoban unit 1 2D PSPACE compl. 1] 15 Puzzle unit 1 2D NP compl. 17] Rush Hour 1 2,3 1 2D PSPACE compl. Atomix unit 1 2D PSPACE compl. [12] 4.2 A Formal De nition of Atomix We will now give a formal de nition of an Atomix problem instance (level ) De nition 1. An Atomix problem instance consists of: A nite set A of so called atom types. A game board B = f0; w 1g f0; h 1g. A bit matrix O = O[p] 2 f0; ....
....is limited by n 2 ; hence, the machine can announce that the puzzle is unsolvable after having applied more moves without nding a solution. Since an encoding of an Atomix state needs only polynomial space, it follows that Atomix is in NPSPACE = PSPACE. ut Very recently, Holzer and Schwoon [12] showed by reduction from non empty intersection of nite automata that Atomix is even PSPACE complete. They also provide a level with an exponentially long optimal solution. 5 Searching the State Space of Atomix Much progress has been made in the area of heuristic search. This is due to: faster ....
M. Holzer and S. Schwoon. Assembling Molecules in Atomix is Hard. Technical Report 0101, Institut fr Informatik, Technische Universitt Mnchen, May 2001.
Prediction of Regular Search Tree Growth by Spectral Analysis - Edelkamp (Correct)
....to derive exact or approximate search tree prediction in this domain. As Andreas Junghanns has coined in his Ph.D. dissertation [8] the impact of the search tree node prediction formula # # ### # ### # (# # #) has still to be shown. In the other PSPACE complete sliding block game Atomix [7, 6] simpli cation based on branching equivalences do apply and yield savings that are exponential in the number of atoms, but this void labeling scheme still results in an intractable size of the equivalence graph structure. Only very small games can be analyzed by this method. 7.2 Pruning When ....
M. Holzer and S. Schwoon. Assembling molecules in Atomix is hard. Technical Report 0101, Institut fur Informatik, Technische Universitat Munchen, 2001.
Finding Optimal Solutions to Atomix - Hüffner, Edelkamp, Fernau.. (2001) (Correct)
....PushPush # # unit # # # # 2D NP hard Push # # # unit # # # # 2D NP hard Sokoban # # 1#2 # # # # 2D PSPACE compl. Sokoban # # unit # # # # 2D PSPACE compl. 1] 15 Puzzle # unit # # # # 2D NP compl. 17] Rush Hour # 1# 2,3 # # # # 2D PSPACE compl. Atomix # unit # # # # 2D PSPACE compl. [12] 4.2 AFormal De nition of Atomix We will now give a formal de nition of an Atomix problem instance (level ) De nition 1. AnAtomix problem instanceconsists of: A nite set # of so called atom types. A game board # # #######################. A bit matrix # #################of size # # # ....
....is limited by # # #; hence, the machine can announce that the puzzle is unsolvable after having applied more moves without nding a solution. Since an encoding of an Atomix state needs only polynomial space, it follows that Atomix is in NPSPACE # PSPACE. ## Very recently, Holzer and Schwoon [12] showed by reduction from non empty intersection of nite automata that Atomix is even PSPACE complete. They also provide a level with an exponentially long optimal solution. 5 Searching the State Space of Atomix Much progress has been made in the area of heuristic search. This is due to: faster ....
M. Holzer and S. Schwoon. Assembling Molecules in Atomix is Hard. Technical Report 0101, Institut fr Informatik, Technische Universitt Mnchen, May 2001.
PushPush-k is PSPACE-Complete - Demaine, Hoffmann, Holzer (2004) Self-citation (Holzer) (Correct)
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Markus Holzer and Stefan Schwoon. Assembling molecules in Atomix is hard. Technical Report TUM-I0101, Technische Universitat Munchen, May 2001.
On the Complexity of Randolph's Robot Game - Engels, Kamphans (2005) (Correct)
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M. Holzer and S. Schwoon. Assembling molecules in Atomix is hard. Theoret. Comput. Sci., 303(3):447--462, 2004. 15
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