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arXiv · 1709.06995

Dependent randomized rounding for clustering and partition systems with knapsack constraints

David G. Harris·Thomas Pensyl·Aravind Srinivasan·Khoa Trinh
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Abstract

Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among the cluster-centers. This, and much more general clustering problems, can be formulated with "knapsack" and "partition" constraints. We develop new randomized algorithms targeting such problems, and study two in particular: multi-knapsack median and multi-knapsack center. Our rounding algorithms give new approximation and pseudo-approximation algorithms for these problems. One key technical tool, which may be of independent interest, is a new tail bound analogous to Feige (2006) for sums of random variables with unbounded variances. Such bounds can be useful in inferring properties of large networks using few samples.

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David G. Harris, Thomas Pensyl, Aravind Srinivasan, Khoa Trinh. 2017-09-20. Dependent randomized rounding for clustering and partition systems with knapsack constraints. https://arxiv.org/abs/1709.06995

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