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Abstract: Introduction Spiral Galaxies puzzles are pencil and paper puzzles which originated in Japan. Each puzzle consists of a grid of squares, and a collection of circles which are the centers of rotationally symmetric polyominoes which tile the grid. The puzzle is to determine the unique tiling with those centers. An example of a Spiral Galaxies puzzle and its solution are shown in Figure 1. Figure 1. A Spiral Galaxies puzzle (left) and its solution (right) We will show that the question of whether... (Update)
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...to a Corral puzzle can be checked in polynomial time. Similar approaches to proving puzzles are NP complete are taken in [1, 2, 4, 5, 7]. Figure 2. A graph (left) and its corresponding Corral blueprint (right) Wires Our wires will be rectangles of width 3 in the Corral...
...a solution to a Pearl puzzle can be checked in polynomial time. Similar approaches to proving puzzles are NP complete are taken in [1 3, 5 7, 10, 1215 ]. The Construction To build a Pearl puzzle that corresponds to a cubic planar graph G, we first draw a rectilinear...
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Pearl Puzzles are NP-complete - Friedman (Correct)
Corral Puzzles are NP-complete - Friedman (Correct)
Active bibliography (related documents): More All
1.6: The Game of Cubic is NP-complete - Friedman (Correct)
1.0: Hard Tiling Problems with Simple Tiles - Moore, Michael (2000) (Correct)
0.2: Pushing Blocks in Gravity is NP-hard - Friedman (Correct)
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0.5: On Sliding Block Puzzles - Karlemo, Östergård (Correct)
0.5: Packing Unit Squares in Squares: A Survey and New Results - Friedman (2002) (Correct)
0.5: Solving Puzzles related to Permutation Groups - Egner, Püschel (Correct)
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2: Computers and Intractibility: A Guide to the Theory of NPCompleteness (context) - Garey, Johnson - 1979
2: Pushing blocks is NP-complete for non-crossing solution paths - Demaine, Hoffman - 2001
2: Minesweeper is NP-complete (context) - Kaye - 2000
BibTeX entry: (Update)
E. Friedman, "Spiral Galaxies Puzzles are NP-complete". preprint. http://citeseer.ist.psu.edu/539318.html More
@misc{ friedman-spiral,
author = "E. Friedman",
title = "Spiral Galaxies Puzzles are NP-complete",
text = "E. Friedman, Spiral Galaxies Puzzles are NP-complete. preprint.",
url = "citeseer.ist.psu.edu/539318.html" }
Citations (may not include all citations):146 Computers and Intractibility: A Guide to the Theory of NP-Co.. (context) - Garey, Johnson - 1979
24 Sokoban is PSPACE-complete - Culberson - 1998
15 Minesweeper is NP-complete (context) - Kaye
12 Complexity of two-dimensional patterns - Lindgren, Moore et al. - 1998
12 Hard Tiling Problems with Simple Tiles - Moore, Robson DBLP
4 Cubic is NP-complete (context) - Friedman
4 Complexity of tile rotation problems (context) - Goles, Rapaport - 1997 ACM DBLP
3 Tiling allowing rotations only (context) - Goles, Rapaport - 1999 ACM DBLP
3 Computational Geometry (context) - Beauquier, Nivat et al. - 1995 ACM DBLP
2 Tilings with bars and satisfaction of Boolean formulas (context) - Rmila - 1996
Documents on the same site (http://www.stetson.edu/~efriedma/vita.html): More
Packing Unit Squares in Squares: A Survey and New Results - Friedman (2002) (Correct)
Hinged Dissection of Polyominoes and Polyforms - Demaine, Demaine, Eppstein.. (1999) (Correct)
Magic Carpets - Friedman, Keith (2000) (Correct)
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