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Wooden Geometric Puzzles: Design and Hardness Proofs

  • Helmut Alt
  • Hans Bodlaender
  • Marc van Kreveld
  • Günter Rote
  • Gerard Tel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4475)

Abstract

We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretical questions. This leads to the search for instances of partition that use only integers and are uniquely solvable. We show that instances of polynomial size exist with this property. This result also holds for partition into k subsets with the same sum: We construct instances of n integers with subset sum O(n k + 1), for fixed k.

Keywords

Partition Problem Hamiltonian Circuit Unique Partition Hardness Proof Solvable Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Helmut Alt
    • 1
  • Hans Bodlaender
    • 2
  • Marc van Kreveld
    • 2
  • Günter Rote
    • 1
  • Gerard Tel
    • 2
  1. 1.Department of Computer Science, Freie Universität BerlinGermany
  2. 2.Department of Information and Computing Sciences, Utrecht UniversityThe Netherlands

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