TY - JOUR

T1 - Swapping labeled tokens on graphs

AU - Yamanaka, Katsuhisa

AU - Demaine, Erik D.

AU - Ito, Takehiro

AU - Kawahara, Jun

AU - Kiyomi, Masashi

AU - Okamoto, Yoshio

AU - Saitoh, Toshiki

AU - Suzuki, Akira

AU - Uchizawa, Kei

AU - Uno, Takeaki

N1 - Funding Information:
We are grateful to Takashi Horiyama, Shin-ichi Nakano and Ryuhei Uehara for their comments on related work and fruitful discussions with them. This work is supported in part by NSF grant CCF-1161626 and DARPA/AFOSR grant FA9550-12-1-0423 , and by MEXT/JSPS KAKENHI , including the ELC project, Grant Numbers 24106010 , 24700130 , 25106502 , 25106504 , 25330003 , 26730001 .
Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/6/27

Y1 - 2015/6/27

N2 - 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.

AB - 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.

KW - Approximation

KW - Complete bipartite graph

KW - Graph algorithm

KW - Sorting network

KW - Tree

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U2 - 10.1016/j.tcs.2015.01.052

DO - 10.1016/j.tcs.2015.01.052

M3 - Article

AN - SCOPUS:84945293281

VL - 586

SP - 81

EP - 94

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -