Core Concepts
Predictions can significantly accelerate the update time of dynamic submodular maximization algorithms by leveraging patterns in dynamic data.
Abstract
The content discusses the use of predictions to enhance dynamic submodular maximization algorithms. It introduces an algorithmic framework that leverages predictions to improve performance guarantees and reduce query complexity. The approach involves precomputations and update phases based on predictions, achieving significant improvements in efficiency and approximation quality.
Key points include:
- Introduction to dynamic submodular maximization.
- Utilizing predictions for faster updates.
- Theoretical analysis of algorithms with predictions.
- Improved versions of precomputation and update routines.
- Achieving strong robustness in solutions.
- Detailed explanation of the full algorithm setup.
The content provides a comprehensive overview of leveraging predictions for optimizing dynamic submodular maximization algorithms.
Stats
Our main result is an algorithm with an O(poly(log η, log w, log k)) amortized update time over the sequence of updates that achieves a 1/2−ǫ approximation in expectation for dynamic monotone submodular maximization under a cardinality constraint k.
For monotone submodular maximization under a cardinality constraint k, there is a dynamic algorithm with predictions that achieves an amortized query complexity during the streaming phase of O(poly(log η, log w, log k)).
The total number of queries performed by UpdateSol during the t − t′ time steps between time t′ and time t is O(u((ηold + w + k) log k, k) · (ηold + w + k) log k).
Quotes
"Can predictions be used to accelerate the update time of dynamic submodular maximization algorithms?"
"Improved running times have been obtained with predictions for matching, hashing, and clustering."