Research map / Learning theory and algorithms / Submodular and game algorithms
Maximization of Approximately Submodular Functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Approximation error epsilon set to 1/k (greedy algorithm on epsilon-approximately submodular function, cardinality constraint) | Greedy algorithm · cardinality-constrained maximization of approximately submodular function | approximation ratio | Helped |
| Error level epsilon set to n^{-1/2} or larger for general monotone submodular functions (lower-bound regime) | Any query algorithm on approximately submodular monotone functions · cardinality-constrained maximization, query complexity | approximation ratio | Hurt |
| Error level epsilon of order 1/k^{1-beta} (above 1/k) for greedy algorithm | Greedy algorithm · additive approximately submodular functions | approximation ratio | Hurt |
| Bounded curvature assumption on the submodular representative f | Algorithm for approximately submodular maximization · cardinality-constrained maximization with constant epsilon | approximation ratio | Helped |
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