Online and incremental algorithms for facility location

Abstract

In the online and incremental variants of Facility Location, the demands arrive one-by-one and must be assigned to an open facility upon arrival, without any knowledge about future demands. In the online variant, the decisions of opening a facility at a particular location and of assigning a demand to some facility are irrevocable. In the incremental variant, the algorithm can also merge existing facilities (and the corresponding demand clusters) with each other, and only the decision of assigning some demands to the same facility is irrevocable. The goal is to maintain, either online or incrementally, a set of facilities and an assignment of the demands to them that minimize the total facility opening cost plus the assignment cost for all demands. In this survey, we discuss the previous work on online and incremental algorithms for Facility Location. In addition to the main results, namely that the competitive ratio for the online variant is Θ(log n log log n ), where n is the number of demands, and that the competitive ratio for the incremental variant is O(1), we discuss all known online and incremental Facility Location algorithms, sketch the intuition behind them and the main ideas of their competitive analysis, and discuss some applications.