11 research outputs found
A New Lower Bound for Classic Online Bin Packing
We improve the lower bound on the asymptotic competitive ratio of any online algorithm for bin packing to above 1.54278. We demonstrate for the first time the advantage of branching and the applicability of full adaptivity in the design of lower bounds for the classic online bin packing problem. We apply a new method for weight based analysis, which is usually applied only in proofs of upper bounds. The values of previous lower bounds were approximately 1.5401 and 1.5403. 漏 2020, Springer Nature Switzerland AG
Online Computation with Untrusted Advice
The advice model of online computation captures a setting in which the
algorithm is given some partial information concerning the request sequence.
This paradigm allows to establish tradeoffs between the amount of this
additional information and the performance of the online algorithm. However, if
the advice is corrupt or, worse, if it comes from a malicious source, the
algorithm may perform poorly. In this work, we study online computation in a
setting in which the advice is provided by an untrusted source. Our objective
is to quantify the impact of untrusted advice so as to design and analyze
online algorithms that are robust and perform well even when the advice is
generated in a malicious, adversarial manner. To this end, we focus on
well-studied online problems such as ski rental, online bidding, bin packing,
and list update. For ski-rental and online bidding, we show how to obtain
algorithms that are Pareto-optimal with respect to the competitive ratios
achieved; this improves upon the framework of Purohit et al. [NeurIPS 2018] in
which Pareto-optimality is not necessarily guaranteed. For bin packing and list
update, we give online algorithms with worst-case tradeoffs in their
competitiveness, depending on whether the advice is trusted or not; this is
motivated by work of Lykouris and Vassilvitskii [ICML 2018] on the paging
problem, but in which the competitiveness depends on the reliability of the
advice. Furthermore, we demonstrate how to prove lower bounds, within this
model, on the tradeoff between the number of advice bits and the
competitiveness of any online algorithm. Last, we study the effect of
randomization: here we show that for ski-rental there is a randomized algorithm
that Pareto-dominates any deterministic algorithm with advice of any size. We
also show that a single random bit is not always inferior to a single advice
bit, as it happens in the standard model