The Online Multi-Commodity Facility Location Problem
Jannik Castenow, Bj\"orn Feldkord, Till Knollmann, Manuel Malatyali,, Friedhelm Meyer auf der Heide

TL;DR
This paper introduces the first online algorithms for the multi-commodity facility location problem, analyzing their competitive ratios and showing how heterogeneity and cost functions affect performance.
Contribution
It provides the first online algorithms for the multi-commodity facility location problem, establishing competitive ratio bounds and analyzing the impact of heterogeneity and cost functions.
Findings
Lower bound on competitive ratio: Ω(√|S| + log n / log log n)
Deterministic algorithm with O(√|S| · log n) competitiveness
Randomized algorithm with O(√|S| · log n / log log n) competitiveness
Abstract
We consider a natural extension to the metric uncapacitated Facility Location Problem (FLP) in which requests ask for different commodities out of a finite set of commodities. Ravi and Sinha (SODA'04) introduced the model as the Multi-Commodity Facility Location Problem (MFLP) and considered it an offline optimization problem. The model itself is similar to the FLP: i.e., requests are located at points of a finite metric space and the task of an algorithm is to construct facilities and assign requests to facilities while minimizing the construction cost and the sum over all assignment distances. In addition, requests and facilities are heterogeneous; they request or offer multiple commodities out of . A request has to be connected to a set of facilities jointly offering the commodities demanded by it. In comparison to the FLP, an algorithm has to decide not only if and where to…
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