Benjamin Hiller

Probabilistic Analysis of Online Bin Coloring Algorithms Via Stochastic Comparison

This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced in [15]. Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm

Reoptimization gaps versus model errors in online-dispatching of service units for ADAC

textsc{GreedyFit}

Dynamic pricing problems with elastic demand

is stochastically better than the performance of the algorithm

Probabilistic alternatives for competitive analysis

textsc{OneBin}

Simple optimality proofs for Least Recently Used in the presence of locality of reference

for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.

Stochastic dominance analysis of online bin coloring algorithms

Under high load, the automated dispatching of service vehicles for the German Automobile Association (ADAC) must reoptimize a dispatch for 100-150 vehicles and 400 requests in about 10s to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within 10s. One way out are simplified reoptimization models. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new models ShadowPrice and ZIBDIPdummy can keep up with ZIBDIP.

On the optimality of least recently used

We consider a dynamic pricing problem for a company that sells a single product to a group of price-sensitive customers over a finite time horizon. The objective is to set the prices over time so as to maximize revenue. Two price-sensitivity models are studied: multiplicative and additive demand change. We develop a polynomial-time algorithm for the multiplicative model. In contrast, we prove that the problem under additive demand change is NP-hard and admits an FPTAS.

Probabilistic analysis of Online Bin Coloring algorithms via stochastic comparison

In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: It sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior, or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.