# Robust Online Algorithms for Dynamic Problems

## TL;DR

This paper introduces a general framework for designing robust online algorithms for dynamic problems, achieving near-optimal competitive ratios with limited migration, and improves existing algorithms for problems like Bin Packing.

## Contribution

The authors present a novel framework that simplifies the creation of robust online algorithms for dynamic problems, extending to high-dimensional packing problems.

## Key findings

- Achieved asymptotic competitive ratio of γ+ε with migration O(1/ε).
- Improved the best known robust algorithms for dynamic generalizations of packing problems.
- First robust algorithm for general d-dimensional Bin Packing and Vector Packing.

## Abstract

Online algorithms that allow a small amount of migration or recourse have been intensively studied in the last years. They are essential in the design of competitive algorithms for dynamic problems, where objects can also depart from the instance. In this work, we give a general framework to obtain so called robust online algorithms for these dynamic problems: these online algorithm achieve an asymptotic competitive ratio of $\gamma+\epsilon$ with migration $O(1/\epsilon)$, where $\gamma$ is the best known offline asymptotic approximation ratio. In order to use our framework, one only needs to construct a suitable online algorithm for the static online case, where items never depart. To show the usefulness of our approach, we improve upon the best known robust algorithms for the dynamic versions of generalizations of Strip Packing and Bin Packing, including the first robust algorithm for general $d$-dimensional Bin Packing and Vector Packing.