  In this paper we propose a novel online deterministic list update algorithm
known as Move-To-Front-or-Logarithmic Position (MFLP). Our proposed algorithm
MFLP achieves a competitive ratio of 2 for larger list with respect to static
optimum offline algorithm, whereas MFLP is not competitive for smaller list. We
also show that MFLP is 2 competitive with respect to dynamic optimum offline
algorithm. Our results open up a new direction of work towards classifying the
online algorithms based on competitive and not competitive.
