The Online Multi-Commodity Facility Location Problem (original) (raw)

On the Facility Location Problem in Online and Dynamic Models

2020

In this paper we study the facility location problem in the online with recourse and dynamic algorithm models. In the online with recourse model, clients arrive one by one and our algorithm needs to maintain good solutions at all time steps with only a few changes to the previously made decisions (called recourse). We show that the classic local search technique can lead to a (1+√2+e)-competitive online algorithm for facility location with only O(log n/e log 1/e) amortized facility and client recourse, where n is the total number of clients arrived during the process. We then turn to the dynamic algorithm model for the problem, where the main goal is to design fast algorithms that maintain good solutions at all time steps. We show that the result for online facility location, combined with the randomized local search technique of Charikar and Guha [Charikar and Guha, 2005], leads to a (1+√2+e)-approximation dynamic algorithm with total update time of O(n²) in the incremental setting...

Profit maximising single competitive facility location in the plane

A single facility has to be located in the plane in competition with fixed existing facilities of similar type. Demand is supposed to be concentrated at a finite number of points, which fully patronise the facility to which it is most attracted. Attraction by a facility is expressed by some general attractiveness of the facility divided by a power of its Euclidean distance to demand. For existing facilities attractiveness is fixed, while the costs connected with the new facility are an increasing function of its attractiveness. Each demand point attracted by the new facility generates a given amount of income. The aim is to find that location for the new facility which maximizes the resulting profits. It is shown that this problem is well-posed under the additional assumption that consumers are novelty oriented, i.e. attraction ties are resolved in favor of the new facility. The problem then reduces to a parametric maxcovering problem with inflated Euclidean distances, which is solv...