Swapping labeled tokens on graphs
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paper.pdf
Description
Accepted version
Size
119.24 KB
Format
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Checksum (MD5)
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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
2015
Journal
Theoretical Computer Science
Publisher
Elsevier BV
Version
Author's final manuscript
Abstract
© 2015 Elsevier B.V. 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(n2) 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. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.TCS.2015.01.052
