
NearlyTight and Oblivious Algorithms for Explainable Clustering
We study the problem of explainable clustering in the setting first form...
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Almost Tight Approximation Algorithms for Explainable Clustering
Recently, due to an increasing interest for transparency in artificial i...
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NearOptimal Schedules for Simultaneous Multicasts
We study the storeandforward packet routing problem for simultaneous m...
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NearOptimal Explainable kMeans for All Dimensions
Many clustering algorithms are guided by certain cost functions such as ...
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Adapting kmeans algorithms for outliers
This paper shows how to adapt several simple and classical samplingbase...
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Generalizing the Sharp Threshold Phenomenon for the Distributed Complexity of the Lovász Local Lemma
Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted ...
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On the price of explainability for some clustering problems
The price of explainability for a clustering task can be defined as the ...
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Nearoptimal Algorithms for Explainable kMedians and kMeans
We consider the problem of explainable kmedians and kmeans introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). In this problem, our goal is to find a threshold decision tree that partitions data into k clusters and minimizes the kmedians or kmeans objective. The obtained clustering is easy to interpret because every decision node of a threshold tree splits data based on a single feature into two groups. We propose a new algorithm for this problem which is Õ(log k) competitive with kmedians with ℓ_1 norm and Õ(k) competitive with kmeans. This is an improvement over the previous guarantees of O(k) and O(k^2) by Dasgupta et al (2020). We also provide a new algorithm which is O(log^3/2 k) competitive for kmedians with ℓ_2 norm. Our first algorithm is nearoptimal: Dasgupta et al (2020) showed a lower bound of Ω(log k) for kmedians; in this work, we prove a lower bound of Ω̃(k) for kmeans. We also provide a lower bound of Ω(log k) for kmedians with ℓ_2 norm.
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