Corpus ID: 81978110

Token Swapping on Trees

@article{Biniaz2019TokenSO,
  title={Token Swapping on Trees},
  author={A. Biniaz and Kshitij Jain and A. Lubiw and Z. Mas{\'a}rov{\'a} and Tillmann Miltzow and D. Mondal and Anurag Murty Naredla and Josef Tkadlec and Alexi Turcotte},
  journal={ArXiv},
  year={2019},
  volume={abs/1903.06981}
}

A. Biniaz, Kshitij Jain, +6 authors Alexi Turcotte

Published 2019

Mathematics, Computer Science

ArXiv

The input to the token swapping problem is a graph with vertices $v_1, v_2, \ldots, v_n$, and $n$ tokens with labels $1, 2, \ldots, n$, one on each vertex. The goal is to get token $i$ to vertex $v_i$ for all $i= 1, \ldots, n$ using a minimum number of \emph{swaps}, where a swap exchanges the tokens on the endpoints of an edge. Token swapping on a tree, also known as "sorting with a transposition tree", is not known to be in P nor NP-complete. We present some partial results: 1. An optimum… CONTINUE READING

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