
A Parameterized Family of MetaSubmodular Functions
Submodular function maximization has found a wealth of new applications ...
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Contrained Generalization For Data Anonymization  A Systematic Search Based Approach
Data generalization is a powerful technique for sanitizing multiattribu...
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Diversity maximization in doubling metrics
Diversity maximization is an important geometric optimization problem wi...
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Adversarially Robust Submodular Maximization under Knapsack Constraints
We propose the first adversarially robust algorithm for monotone submodu...
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Maximizing diversity over clustered data
Maximum diversity aims at selecting a diverse set of highquality object...
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Constructing Topk Routes with Personalized Submodular Maximization of POI Features
We consider a practical topk route problem: given a collection of point...
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Incorporating Diversity into Influential Node Mining
Diversity is a crucial criterion in many ranking and mining tasks. In th...
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A General CoresetBased Approach to Diversity Maximization under Matroid Constraints
Diversity maximization is a fundamental problem in web search and data mining. For a given dataset S of n elements, the problem requires to determine a subset of S containing k≪ n "representatives" which minimize some diversity function expressed in terms of pairwise distances, where distance models dissimilarity. An important variant of the problem prescribes that the solution satisfy an additional orthogonal requirement, which can be specified as a matroid constraint (i.e., a feasible solution must be an independent set of size k of a given matroid). While unconstrained diversity maximization admits efficient coresetbased strategies for several diversity functions, known approaches dealing with the additional matroid constraint apply only to one diversity function (sum of distances), and are based on an expensive, inherently sequential, local search over the entire input dataset. We devise the first coresetbased algorithms for diversity maximization under matroid constraints for various diversity functions, together with efficient sequential, MapReduce and Streaming implementations. Technically, our algorithms rely on the construction of a small coreset, that is, a subset of S containing a feasible solution which is no more than a factor 1ϵ away from the optimal solution for S. While our algorithms are fully general, for the partition and transversal matroids, if ϵ is a constant in (0,1) and S has bounded doubling dimension, the coreset size is independent of n and it is small enough to afford the execution of a slow sequential algorithm to extract a final, accurate, solution in reasonable time. Extensive experiments show that our algorithms are accurate, fast and scalable, and therefore they are capable of dealing with the large input instances typical of the big data scenario.
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