CS Theory Seminar at IIT Delhi

Publications:

A Tight Lower Bound Instance for k-means++ in Constant Dimension in TAMC 2014 (with Ragesh Jaiswal and Nir Ailon)

Sampling in Space Restricted Settings in COCOON 2015 (with Davis Issac, Ragesh Jaiswal and Amit Kumar) Slides(PPTX)

We consider the random sampling problem in the streaming setting. The algorithm returns, at any time t, an item chosen uniformly at random from all items seen till time t. Our model allows storage for only one item at a time in the stream. We design an algorithm that takes O(log n) random bits and O(log n) space to maintain a random sample at all times. Our algorithm in the streaming setting matches the lower bound on the amount of required randomness for uniform sampling in the offline setting. We also extend the work on sampling in the query model by Bringmann and Larsen (STOC 2013) to the approximate setting and obtain almost matching upper and lower bounds for the problem.

Faster Algorithms for the Constrained k-means Problem in STACS 2016 (with Ragesh Jaiswal and Amit Kumar) Slides (PDF)