Swapping Labeled Tokens on Graphs
Author(s)
Yamanaka, Katsuhisa; Demaine, Erik D.; Ito, Takehiro; Kawahara, Jun; Kiyomi, Masashi; Okamoto, Yoshio; Saitoh, Toshiki; Suzuki, Akira; Uchizawa, Kei; Uno, Takeaki; ... Show more Show less
DownloadDemaine_Swapping labeled.pdf (119.2Kb)
OPEN_ACCESS_POLICY
Open Access Policy
Creative Commons Attribution-Noncommercial-Share Alike
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2014Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
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
ISBN
978-3-319-07889-2
978-3-319-07890-8
ISSN
0302-9743
1611-3349