
Improved MultiPass Streaming Algorithms for Submodular Maximization with Matroid Constraints
We give improved multipass streaming algorithms for the problem of maxi...
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An Optimal Streaming Algorithm for Nonmonotone Submodular Maximization
We study the problem of maximizing a nonmonotone submodular function su...
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Submodular Streaming in All its Glory: Tight Approximation, Minimum Memory and Low Adaptive Complexity
Streaming algorithms are generally judged by the quality of their soluti...
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SemiStreaming Algorithms for Submodular Matroid Intersection
While the basic greedy algorithm gives a semistreaming algorithm with a...
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Streaming Robust Submodular Maximization: A Partitioned Thresholding Approach
We study the classical problem of maximizing a monotone submodular funct...
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The Oneway Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness
We consider the classical problem of maximizing a monotone submodular fu...
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ONCE and ONCE+: Counting the Frequency of Timeconstrained Serial Episodes in a Streaming Sequence
As a representative sequential pattern mining problem, counting the freq...
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Streaming Submodular Maximization with Matroid and Matching Constraints
Recent progress in (semi)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural generalizations such as matroid and matching constraints. This paper aims at closing this gap. For a single matroid of rank k (i.e., any solution has cardinality at most k), our main results are: ∙ A singlepass streaming algorithm that uses O(k) memory and achieves an approximation guarantee of 0.3178. ∙ A multipass streaming algorithm that uses O(k) memory and achieves an approximation guarantee of (11/e  ε) by taking constant number of passes over the stream. This improves on the previously best approximation guarantees of 1/4 and 1/2 for singlepass and multipass streaming algorithms, respectively. In fact, our multipass streaming algorithm is tight in that any algorithm with a better guarantee than 1/2 must make several passes through the stream and any algorithm that beats our guarantee 11/e must make linearly many passes. For the problem of maximizing a monotone submodular function subject to a bipartite matching constraint (which is a special case of matroid intersection), we show that it is not possible to obtain better than 0.3715approximation in a single pass, which improves over a recent inapproximability of 0.522 for this problem. Furthermore, given a plausible assumption, our inapproximability result improves to 1/3 ≈ 0.333.
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