Linear-Time Algorithm for Sliding Tokens on Trees

Suppose that we are given two independent sets I [subscript b] and I [subscript r] of a graph such that ∣ I [subscript b] ∣ = ∣ I [subscript r] ∣, and imagine that a token is placed on each vertex in I [subscript b]. Then, the sliding token problem is to determine whether there exists a sequence of...

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Main Authors: Demaine, Erik D. (Contributor), Demaine, Martin L. (Contributor), Fox-Epstein, Eli (Author), Hoang, Duc A. (Author), Ito, Takehiro (Author), Ono, Hirotaka (Author), Otachi, Yota (Author), Uehara, Ryuhei (Author), Yamada, Takeshi (Author)
Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
Format: Article
Language:English
Published: Springer-Verlag, 2015-11-23T14:48:03Z.
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Online Access:Get fulltext
LEADER 02368 am a22003253u 4500
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042 |a dc 
100 1 0 |a Demaine, Erik D.  |e author 
100 1 0 |a Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory  |e contributor 
100 1 0 |a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science  |e contributor 
100 1 0 |a Demaine, Erik D.  |e contributor 
100 1 0 |a Demaine, Martin L.  |e contributor 
700 1 0 |a Demaine, Martin L.  |e author 
700 1 0 |a Fox-Epstein, Eli  |e author 
700 1 0 |a Hoang, Duc A.  |e author 
700 1 0 |a Ito, Takehiro  |e author 
700 1 0 |a Ono, Hirotaka  |e author 
700 1 0 |a Otachi, Yota  |e author 
700 1 0 |a Uehara, Ryuhei  |e author 
700 1 0 |a Yamada, Takeshi  |e author 
245 0 0 |a Linear-Time Algorithm for Sliding Tokens on Trees 
246 3 3 |a Polynomial-Time Algorithm for Sliding Tokens on Trees 
260 |b Springer-Verlag,   |c 2015-11-23T14:48:03Z. 
856 |z Get fulltext  |u http://hdl.handle.net/1721.1/99985 
520 |a Suppose that we are given two independent sets I [subscript b] and I [subscript r] of a graph such that ∣ I [subscript b] ∣ = ∣ I [subscript r] ∣, and imagine that a token is placed on each vertex in I [subscript b]. Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms I [subscript b] and I [subscript r] so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in the graph. This problem is known to be PSPACE-complete even for planar graphs, and also for bounded treewidth graphs. In this paper, we show that the problem is solvable for trees in quadratic time. Our proof is constructive: for a yes-instance, we can find an actual sequence of independent sets between I [subscript b] and I [subscript r] whose length (i.e., the number of token-slides) is quadratic. We note that there exists an infinite family of instances on paths for which any sequence requires quadratic length. 
520 |a National Science Foundation (U.S.) (Grant CCF-1161626) 
520 |a United States. Defense Advanced Research Projects Agency (United States. Air Force Office of Scientific Research Grant FA9550-12-1-0423) 
546 |a en_US 
655 7 |a Article 
773 |t Algorithms and Computation