Research map / Learning theory and algorithms / Submodular and game algorithms
Robust Sequence Submodular Maximization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a two-stage greedy construction that selects the first τ elements and then greedily selects the rest independently of that prefix | Robust sequence maximization with contiguous removals · Robust sequence maximization, contiguous removals | approximation ratio: \max \left \{ \frac{(e - 1)^2}{e(2e-1)}, \frac{(e - 1)(e^{\frac{k-2\tau}{k-\tau}} -1)}{(2e - 1)e^{\frac{k-2\tau}{k-\tau} | Helped |
| Choose the first τ elements by absolute value instead of marginal value | Robust sequence maximization with arbitrary removals · Robust sequence maximization, arbitrary removals | approximation ratio: \frac{1- 1/e}{1 + \tau} | Helped |
| Apply ordinary Sequence Submodular Greedy directly to the robust objective | Robust sequence maximization · Robust sequence maximization | robust objective value | Hurt |
| Require general-sequence-submodularity rather than sequence-submodularity for arbitrary-removal robustness | Arbitrary-removal robust greedy · Robust sequence maximization, arbitrary removals | approximation ratio: \frac{1- 1/e}{1 + \tau} | Helped |
| Relax exact sequence-submodularity and backward-monotonicity to approximate versions | Proposed robust greedy algorithms · Robust sequence maximization under approximate assumptions | approximation ratio: \frac{\alpha^2 \mu_1 \mu_3 (e^{\mu_1} - 1)}{(\mu_1 + \alpha \tau)e^{\mu_1}} | Helped |
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