Erik D. Demaine and Michael Ho#mann. Pushing blocks is NPcomplete for noncrossing solution paths. In Proceedings of the 13th Canadian Conference on Computational Geometry, pages 65--68, Waterloo, Canada, August 2001. http://compgeo.math.uwaterloo. ca/~cccg01/proceedings/long/eddemaine-24711.ps. 13  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Blocks in Gravity is NP hard Erich Friedman Stetson University, DeLand, FL 32720 efriedma stetson.edu Introduction There has been much progress recently showing that certain classes of puzzles involving pushing blocks [2, 3, 4, 10] are NP hard. For example, consider the block pushing puzzle Push k which consists of movable unit square blocks on an integer lattice, and a robot that can move horizontally and vertically to attempt to reach a specified lattice position. The robot can push k blocks provided it pushes them to ....

....For example, consider the block pushing puzzle Push k which consists of movable unit square blocks on an integer lattice, and a robot that can move horizontally and vertically to attempt to reach a specified lattice position. The robot can push k blocks provided it pushes them to open squares. In [4], the authors prove that Push k is NP hard using a reduction from the 3 coloring of planar graphs. That is, for a given planar graph, they build a Push k puzzle that can be solved if and only if the vertices of the original graph can be 3 colored. As 3 colorability is NP hard [9] so is Push k. ....

E. D. Demaine and M. Hoffman, "Pushing blocks is NP-complete for non-crossing solution paths". Proc. 13th Canad. Conf. Comput. Geom. (2001), 65-68.

....cubic planar graph has a Hamiltonian circuit is known to be NP complete [8, 9] this will show that Pearl puzzles are NP hard. We complete the proof by verifying that 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 realization G of G. That is, G is a drawing of G with all edges made of horizontal and vertical line segments. For example, the cubic graph on the left in Figure 2 has the ....

E. D. Demaine and M. Hoffman, "Pushing blocks is NP-complete for non-crossing solution paths". Proc. 13th Canad. Conf. Comput. Geom. (2001), 65-68.

....Since 3 colorability of planar graphs is known to be NP complete [6] this will show that Corral puzzles are NP hard. We complete the proof by showing that a solution 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 puzzle, with every fourth row containing 2 in the left column and 12 in the middle column. A wire can be locally solved in essentially 3 different ways, as shown ....

E. D. Demaine and M. Hoffman, "Pushing blocks is NP-complete for non-crossing solution paths". Proc. 13th Canad. Conf. Comput. Geom. (2001), 65-68.

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Erik D. Demaine and Michael Ho#mann. Pushing blocks is NPcomplete for noncrossing solution paths. In Proceedings of the 13th Canadian Conference on Computational Geometry, pages 65--68, Waterloo, Canada, August 2001. http://compgeo.math.uwaterloo. ca/~cccg01/proceedings/long/eddemaine-24711.ps. 13

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E. D. Demaine and M. Homann. Pushing blocks is NP-complete for noncrossing solution paths. In Proc. 13th Canadian Conf. Comput. Geom., 2001. To appear.

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