Efficient fully dynamic load balancing with approximation better than the known barrier

Determine whether there exists an efficient fully dynamic load-balancing algorithm with an $O(1)$- or even polylogarithmic approximation, or establish conditional lower bounds showing that such approximation guarantees are impossible.

Background

The paper establishes strong results for incremental and decremental load balancing but does not resolve the fully dynamic setting. A conditional lower bound rules out a $(2-\Omega(1))$-approximation with sufficiently small update time even for unweighted graphs, while the status of approximation factors at or above $2$ remains unresolved.

The authors emphasize that matching no longer presents the same barrier for this regime because efficient fully dynamic $2$-approximate matching is known. The open problem is therefore specifically whether fully dynamic load balancing admits efficient constant-factor or polylogarithmic approximation algorithms, or whether stronger conditional lower bounds exist.