Related papers: Computational bounds on randomized algorithms for …
Computing lower and upper bounds on the competitive ratio of online algorithms is a challenging question: For a minimization combinatorial problem, proving a competitive ratio for a given algorithm leads to an upper bound. However computing…
Online bin stretching is an online packing problem where some of the best known lower and upper bounds were found through computational searches. The limiting factor in obtaining better bounds with such methods is the computational time…
Bin packing is a classic optimization problem with a wide range of applications, from load balancing to supply chain management. In this work, we study the online variant of the problem, in which a sequence of items of various sizes must be…
Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance…
We present an algorithm for computing upper bounds for the Online Bin Stretching Problem with a small number of bins and the resulting upper bounds for 4, 5 and 6 bins. This both demonstrates the possibility of using computer search for…
We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the…
There are several problems in the theory of online computation where tight lower bounds on the competitive ratio are unknown and expected to be difficult to describe in a short form. A good example is the Online Bin Stretching problem, in…
The online assignment problem plays an important role in operational research and computer science which is why immense attention has been given to improving its solution quality. Due to the incomplete information about the input, it is…
Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking,…
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…
Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking,…
In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the…
In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…
e consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and in turn, improved decision making. In…
Online bidding is a classical problem in online decision-making, with applications in resource allocation, hierarchical clustering, and the analysis of approximation algorithms. We study its randomized learning-augmented variant, where an…
We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio…
We analyze Decentralized Online Optimization algorithms using the Performance Estimation Problem approach which allows, to automatically compute exact worst-case performance of optimization algorithms. Our analysis shows that several…
We show how to restrict the analysis of a class of online problems that includes the $k$-server problem in finite metrics such that we only have to consider finite sequences of request. When applying the restrictions, both the optimal…