  We construct a deterministic 4-competitive algorithm for the online file
migration problem, beating the currently best 20-year-old, 4.086-competitive
MTLM algorithm by Bartal et al. (SODA 1997). Like MTLM, our algorithm also
operates in phases, but it adapts their lengths dynamically depending on the
geometry of requests seen so far. The improvement was obtained by carefully
analyzing a linear model (factor-revealing LP) of a single phase of the
algorithm. We also show that if an online algorithm operates in phases of fixed
length and the adversary is able to modify the graph between phases, then the
competitive ratio is at least 4.086.
