Solving General Lattice Puzzles

  • Gill Barequet
  • Shahar Tal
Conference paper

DOI: 10.1007/978-3-642-14553-7_14

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6213)
Cite this paper as:
Barequet G., Tal S. (2010) Solving General Lattice Puzzles. In: Lee DT., Chen D.Z., Ying S. (eds) Frontiers in Algorithmics. FAW 2010. Lecture Notes in Computer Science, vol 6213. Springer, Berlin, Heidelberg


In this paper we describe implementations of two general methods for solving puzzles on any structured lattice. We define the puzzle as a graph induced by (finite portion of) the lattice, and apply a back-tracking method for iteratively find all solutions by identifying parts of the puzzle (or transformed versions of them) with subgraphs of the puzzle, such that the entire puzzle graph is covered without overlaps by the graphs of the parts. Alternatively, we reduce the puzzle problem to a submatrix-selection problem, and solve the latter problem by using the “dancing-links” trick of Knuth. A few expediting heuristics are discussed, and experimental results on various lattice puzzles are presented.


Polyominoes polycubes 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gill Barequet
    • 1
  • Shahar Tal
    • 2
  1. 1.Center for Graphics and Geometric Computing, Dept. of Computer Science, TechnionIsrael Institute of TechnologyHaifaIsrael
  2. 2.Dept. of Computer ScienceThe Open UniversityRaananaIsrael

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