News/blog Contact

Online Multi-Coloring on the Path Revisited.
Marie G. Christ, Lene M. Favrholdt, and Kim S. Larsen.
Acta Informatica, 50(5-6): 343-357, 2013.
Multi-coloring on the path is a model for frequency assignment in linear cellular networks. Two models have been studied in previous papers: calls may either have finite or infinite duration. For hexagonal networks, a variation of the models where limited frequency reassignment is allowed has also been studied.

We add the concept of frequency reassignment to the models of linear cellular networks and close these problems by giving matching upper and lower bounds in all cases. We prove that no randomized algorithm can have a better competitive ratio than the best deterministic algorithms. In addition, we give an exact characterization of the natural greedy algorithms for these problems.

All of the above results are with regard to competitive analysis. Taking steps towards a more fine-grained analysis, we consider the case of finite calls and no frequency reassignment and prove that, even though randomization cannot bring the competitive ratio down to one, it seems that the greedy algorithm is expected optimal on uniform random request sequences. We prove this for small paths and indicate it experimentally for larger graphs.


publication
Link to the publication at the publisher's site - subscription may be required.
Text required by the publisher (if any): The final publication is available at link.springer.com.

open access (129 KB)
The same as the publisher's version, when the publisher permits. Otherwise, the author's last version before the publisher's copyright; this is often exactly the same, but sometimes fonts, page numbers, figure numbers, etc. are different. It may also be a full version. However, it is safe to read this version, and at the same time cite the official version, as long as references to concrete locations, numbered theorems, etc. inside the article are avoided.

other publications
Other publications by the author.