Online Multi-Coloring on the Path Revisited

Marie Gabriele Christ, Lene Monrad Favrholdt, Kim Skak Larsen

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalActa Informatica
Issue number5/6
Pages (from-to)343-357
Publication statusPublished - 2013


Dive into the research topics of 'Online Multi-Coloring on the Path Revisited'. Together they form a unique fingerprint.

Cite this