DeepAI AI Chat
Log In Sign Up

Online Bin Covering with Limited Migration

04/13/2019
by   Sebastian Berndt, et al.
0

Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor β: When an object o of size s(o) arrives, the decisions for objects of total size at most β· s(o) may be revoked. Usually β should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classic problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective. In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small ). We therefore resolve the competitiveness of the bin covering problem with migration.

READ FULL TEXT
05/20/2019

Robust Online Algorithms for Dynamic Problems

Online algorithms that allow a small amount of migration or recourse hav...
04/20/2021

Robust Online Algorithms for Dynamic Choosing Problems

Semi-online algorithms that are allowed to perform a bounded amount of r...
04/30/2019

Online Bin Covering with Advice

The bin covering problem asks for covering a maximum number of bins with...
02/18/2021

Locality in Online Algorithms

Online algorithms make decisions based on past inputs. In general, the d...
09/01/2022

Online Load Balancing on Uniform Machines with Limited Migration

In the problem of online load balancing on uniformly related machines wi...
10/01/2021

Online Primal-Dual Algorithms with Predictions for Packing Problems

The domain of online algorithms with predictions has been extensively st...
11/17/2022

Covering and packing with homothets of limited capacity

This work revolves around the two following questions: Given a convex bo...