- 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.
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