Chapter

Frontiers in Algorithmics

Volume 6213 of the series Lecture Notes in Computer Science pp 124-135

Solving General Lattice Puzzles

  • Gill BarequetAffiliated withCenter for Graphics and Geometric Computing, Dept. of Computer Science, Technion, Israel Institute of Technology
  • , Shahar TalAffiliated withDept. of Computer Science, The Open University

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Abstract

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.

Keywords

Polyominoes polycubes