Approximation gap for PSIP-DG

Close the gap between the known approximation algorithms and inapproximability bounds for the Project Scheduling Interdiction Problem with Delay Groups, either by proving tighter lower bounds for specific project network classes such as series-parallel or sparse PERT networks or by designing algorithms with improved worst-case guarantees.

Background

The paper establishes a greedy k-approximation algorithm for PSIP-DG with budgeted uncertainty and an inapproximability bound of 1-1/e+ε for a general variant. These results leave a substantial theoretical gap between achievable approximation performance and hardness of approximation.

The authors identify tighter lower bounds for restricted project-network classes and stronger approximation algorithms as two possible routes toward resolving this gap.

References

Several open problems arise naturally from this work. Our hardness results leave a gap between known approximation algorithms and inapproximability bounds. Closing this gap, either by proving tighter lower bounds for specific project network classes (for example series-parallel or sparse PERT networks) or by designing algorithms with improved worst-case guarantees, would be an interesting challenge.

— The Project Scheduling Interdiction Problem with Delay Groups  (2608.27386 - Wu et al., 27 Aug 2026) in Section Conclusions