Research map / Learning theory and algorithms / Submodular and game algorithms
Fully Dynamic Submodular Maximization over Matroids
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Maintain a multilevel data structure that reorders and delays low-robustness additions and swaps | Fully dynamic matroid submodular maximization · Fully dynamic monotone submodular maximization under a matroid constraint | approximation factor: 4-approximation | Helped |
| Maintain a multilevel data structure and simulate the Swapping algorithm through delayed processing | Fully dynamic matroid submodular maximization · Fully dynamic monotone submodular maximization under a matroid constraint | expected amortized update time: O(k^2\log k \log^2 \Delta \log^2 n) | Helped |
| Use geometric thresholds and parallel copies to remove dependence on Δ | Proposed dynamic algorithm · Fully dynamic monotone submodular maximization under a matroid constraint | expected amortized update time: O\left(\frac {k^2}\varepsilon \log k \log^2 n \log^3 \frac k \varepsilon\right) | Helped |
| Recompute the solution from scratch after deletions using Dynamic-Swapping | Dynamic-Swapping · Constructed additive instance, cardinality constraint k=1 | amortized update time: \Omega(n) | Hurt |
| Recompute the solution from scratch after insertions and deletions using Dynamic-Greedy | Dynamic-Greedy · Constructed additive instance, cardinality constraint k=1 | amortized update time: \Omega(n) | Hurt |
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