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DOI: 10.4230/LIPIcs.ESA.2016.66
URN: urn:nbn:de:0030-drops-64084
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6408/
Miltzow, Tillmann ; Narins, Lothar ; Okamoto, Yoshio ; Rote, Günter ; Thomas, Antonis ; Uno, Takeaki
Approximation and Hardness of Token Swapping
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Abstract
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
@InProceedings{miltzow_et_al:LIPIcs:2016:6408,
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 = {http://drops.dagstuhl.de/opus/volltexte/2016/6408},
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 | |
| Seminar: | 24th Annual European Symposium on Algorithms (ESA 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 18.08.2016 |
