Swapping Labeled Tokens on Graphs

  • Katsuhisa Yamanaka
  • Erik D. Demaine
  • Takehiro Ito
  • Jun Kawahara
  • Masashi Kiyomi
  • Yoshio Okamoto
  • Toshiki Saitoh
  • Akira Suzuki
  • Kei Uchizawa
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8496)


Consider a puzzle consisting of n tokens on an n-vertex graph, where each token has a distinct starting vertex and a distinct target vertex it wants to reach, and the only allowed transformation is to swap the tokens on adjacent vertices. We prove that every such puzzle is solvable in O(n 2) token swaps, and thus focus on the problem of minimizing the number of token swaps to reach the target token placement. We give a polynomial-time 2-approximation algorithm for trees, and using this, obtain a polynomial-time 2α-approximation algorithm for graphs whose tree α-spanners can be computed in polynomial time. Finally, we show that the problem can be solved exactly in polynomial time on complete bipartite graphs.


Polynomial Time Complete Bipartite Graph Directed Cycle Unweighted Graph Sorting Network 
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 International Publishing Switzerland 2014

Authors and Affiliations

  • Katsuhisa Yamanaka
    • 1
  • Erik D. Demaine
    • 2
  • Takehiro Ito
    • 3
  • Jun Kawahara
    • 4
  • Masashi Kiyomi
    • 5
  • Yoshio Okamoto
    • 6
  • Toshiki Saitoh
    • 7
  • Akira Suzuki
    • 3
  • Kei Uchizawa
    • 8
  • Takeaki Uno
    • 9
  1. 1.Iwate UniversityJapan
  2. 2.Massachusetts Institute of TechnologyUSA
  3. 3.Tohoku UniversityJapan
  4. 4.Nara Institute of Science and TechnologyJapan
  5. 5.Yokohama City UniversityJapan
  6. 6.University of Electro-CommunicationsJapan
  7. 7.Kobe UniversityJapan
  8. 8.Yamagata UniversityJapan
  9. 9.National Institute of InformaticsJapan

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