License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2016.66
URN: urn:nbn:de:0030-drops-64084
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Miltzow, Tillmann ; Narins, Lothar ; Okamoto, Yoshio ; Rote, G√ľnter ; Thomas, Antonis ; Uno, Takeaki

Approximation and Hardness of Token Swapping

LIPIcs-ESA-2016-66.pdf (0.5 MB)


Given a graph G=(V,E) with V={1,...,n}, we place on every vertex a token T_1,...,T_n. A swap is an exchange of tokens on adjacent vertices. We consider the algorithmic question of finding a shortest sequence of swaps such that token T_i is on vertex i. We are able to achieve essentially matching upper and lower bounds, for exact algorithms and approximation algorithms. For exact algorithms, we rule out any 2^{o(n)} algorithm under the ETH. This is matched with a simple 2^{O(n*log(n))} algorithm based on a breadth-first search in an auxiliary graph. We show one general 4-approximation and show APX-hardness. Thus, there is a small constant delta > 1 such that every polynomial time approximation algorithm has approximation factor at least delta.

Our results also hold for a generalized version, where tokens and vertices are colored. In this generalized version each token must go to a vertex with the same color.

BibTeX - Entry

  author =	{Tillmann Miltzow and Lothar Narins and Yoshio Okamoto and G{\"u}nter Rote and Antonis Thomas and Takeaki Uno},
  title =	{{Approximation and Hardness of Token Swapping}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{66:1--66:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-64084},
  doi =		{10.4230/LIPIcs.ESA.2016.66},
  annote =	{Keywords: token swapping, minimum generator sequence, graph theory, NP-hardness, approximation algorithms}

Keywords: token swapping, minimum generator sequence, graph theory, NP-hardness, approximation algorithms
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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