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Fast algorithms for maximizing submodular functions
TLDR
A new variant of the continuous greedy algorithm, which interpolates between the classical greedy algorithm and a truly continuous algorithm, is developed, which can be implemented for matroid and knapsack constraints using O(n2) oracle calls to the objective function. Expand
Streaming submodular maximization: massive data summarization on the fly
TLDR
This paper develops the first efficient streaming algorithm with constant factor 1/2-ε approximation guarantee to the optimum solution, requiring only a single pass through the data, and memory independent of data size. Expand
Lazier Than Lazy Greedy
TLDR
The first linear-time algorithm for maximizing a general monotone submodular function subject to a cardinality constraint is developed, and it is shown that the randomized algorithm, STOCHASTIC-GREEDY, can achieve a (1 — 1/e — e) approximation guarantee, in expectation, to the optimum solution in time linear in the size of the data. Expand
Bandits with Knapsacks
TLDR
This work presents two algorithms whose reward is close to the information-theoretic optimum: one is based on a novel "balanced exploration" paradigm, while the other is a primal-dual algorithm that uses multiplicative updates that is optimal up to polylogarithmic factors. Expand
Fast Constrained Submodular Maximization: Personalized Data Summarization
TLDR
The first practical and FAst coNsTrained submOdular Maximization algorithm, FANTOM, is developed with strong theoretical guarantees, and it is observed that FANTOM constantly provides the highest utility against all the baselines. Expand
Resourceful Contextual Bandits
TLDR
This work designs the first algorithm for solving contextual bandits with ancillary constraints on resources that handles constrained resources other than time, and improves over a trivial reduction to the non-contextual case. Expand
Sketching valuation functions
TLDR
It is proved that every deterministic algorithm that accesses the function via value queries only cannot guarantee a sketching ratio better than n1−e, and it is shown that coverage functions, an interesting subclass of submodular functions, admit arbitrarily good sketches. Expand
Learning on a budget: posted price mechanisms for online procurement
TLDR
This work presents a constant-competitive posted price mechanism when agents are identically distributed and the buyer has a symmetric submodular utility function and gives a truthful mechanism that is O(1)-competitive but uses bidding rather than posted pricing. Expand
Buyback Problem - Approximate Matroid Intersection with Cancellation Costs
TLDR
This work gives a deterministic algorithm for the case when the constraint is an intersection of k matroid constraints and proves a matching lower bound on the competitive ratio for this problem and extends the results to arbitrary downward closed set systems. Expand
Approximating low-dimensional coverage problems
TLDR
A fixed-parameter tractable approximation scheme that outputs a (1-ε)-approximation to the maximum-cardinality union of k sets, in running time, and an improved upper bound on the approximation ratio of the greedy algorithm in special cases of the problem, including when the sets have bounded cardinality and when they are two-dimensional halfspaces. Expand
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