Swapping Labeled Tokens on Graphs
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Demaine_Swapping labeled.pdf
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119.25 KB
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Author(s)
Yamanaka, Katsuhisa
Demaine, Erik D.
Ito, Takehiro
Kawahara, Jun
Kiyomi, Masashi
Okamoto, Yoshio
Saitoh, Toshiki
Suzuki, Akira
Uchizawa, Kei
Uno, Takeaki
Date Issued
2014
Journal
Fun with Algorithms
Publisher
Springer-Verlag
Citation
Yamanaka, Katsuhisa, Erik D. Demaine, Takehiro Ito, Jun Kawahara, Masashi Kiyomi, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Kei Uchizawa, and Takeaki Uno. “Swapping Labeled Tokens on Graphs.” Fun with Algorithms (2014): 364–375.
Version
Author's final manuscript
Abstract
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 [superscript 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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/978-3-319-07890-8_31
