Token swapping on trees

A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv:1903.06981 (n.d.).

Preprint | Submitted | English
Biniaz, Ahmad; Jain, Kshitij; Lubiw, Anna; Masárová, ZuzanaIST Austria ; Miltzow, Tillmann; Mondal, Debajyoti; Naredla, Anurag Murty; Tkadlec, PepaIST Austria; Turcotte, Alexi
The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of 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 swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.
Publishing Year
Date Published
Journal Title

Cite this

Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv:190306981.
Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. ArXiv:1903.06981. ArXiv.
Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv:1903.06981. ArXiv, n.d.
A. Biniaz et al., “Token swapping on trees,” arXiv:1903.06981. ArXiv.
Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv:1903.06981.
Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv:1903.06981, ArXiv.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access
Material in IST:
Dissertation containing IST record


Marked Publications

Open Data IST Research Explorer


arXiv 1903.06981

Search this title in

Google Scholar