@inbook{b975cfdf890941b28fdfc2c0f24b1161,

title = "Polynomial-time algorithm for sliding tokens on trees",

abstract = "Suppose that we are given two independent sets I b and Ir of a graph such that |Ib| = | Ir|, and imagine that a token is placed on each vertex in I b. Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms Ib and I 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 Ib and Ir 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.",

author = "Demaine, {Erik D.} and Demaine, {Martin L.} and Eli Fox-Epstein and Hoang, {Duc A.} and Takehiro Ito and Hirotaka Ono and Yota Otachi and Ryuhei Uehara and Takeshi Yamada",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

year = "2014",

doi = "10.1007/978-3-319-13075-0_31",

language = "English",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "389--400",

editor = "Hee-Kap Ahn and Chan-Su Shin",

booktitle = "Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings",

address = "Germany",

}