Online Facility Location in Evolving Metrics

The Dynamic Facility Location problem is a generalization of the classic problem, in which distance metric between clients and facilities changes over time. Such metrics that develop as function time are usually called “evolving metrics”, thus can be alternatively interpreted evolving metrics. objective this time-dependent variant to balance trade-off optimizing stability solution, modeled by charging switching cost when client’s assignment from one facility another. In paper, we study online Location. We present randomized O(logm+logn)-competitive algorithm, where m number n clients. first step, our algorithm produces fractional each timestep, involving regularization function. This step an adaptation generic proposed Buchbinder et al. their work “Competitive Analysis via Regularization.” Then, rounds solution timestep integral with use exponential clocks. complement result proving lower bound Ω(m) for deterministic algorithms Ω(logm) algorithms. To best knowledge, these results problem.