Name
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 u003e 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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.4230/LIPIcs.ESA.2016.66 | european symposium on algorithms |
Field | DocType | Citations |
Approximation algorithm,Binary logarithm,Swap (computer programming),Graph,Discrete mathematics,Combinatorics,Vertex (geometry),Upper and lower bounds,Neighbourhood (graph theory),Security token,Mathematics | Conference | 1 |
PageRank | References | Authors |
0.36 | 0 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tillmann Miltzow | 1 | 37 | 16.31 |
| Lothar Narins | 2 | 1 | 0.36 |
| Yoshio Okamoto | 3 | 170 | 28.50 |
| Günter Rote | 4 | 1181 | 129.29 |
| Antonis Thomas | 5 | 1 | 0.69 |
| Takeaki Uno | 6 | 1319 | 107.99 |