Restricting-update algorithms for mixed packing-covering linear programs

Develop non-trivial algorithms for maintaining approximate solutions to mixed packing-covering linear programs under restricting, or decremental, updates.

Background

Prior work had established near-optimal algorithms for maintaining (1+ϵ)(1+\epsilon)-approximate solutions to mixed packing-covering linear programs under relaxing, or incremental, updates. The corresponding problem under restricting, or decremental, updates was unresolved.

Dynamic load balancing is described as one of the most basic mixed packing-covering LP instances. The paper supplies a near-optimal decremental algorithm for this special case, which the authors characterize as a first step toward the broader unresolved problem rather than a complete resolution.

References

showed how to maintain a $(1+)$-approximate solution of mixed packing-covering LPs under relaxing (i.e.~incremental) updates in near-optimal update time, and left as an open problem whether non-trivial algorithms exist for ``restricting'' (i.e.~decremental) updates.

— Dynamic Load Balancing under Restricting Updates  (2610.23768 - Bernstein et al., 16 Oct 2026) in Section 1, Related Work: Mixed packing-covering LP