Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, March 26, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: https://ethz.zoom.us/j/563801169

Speaker: Julian Portmann

k-means++: few more steps yield constant approximation

The talk was recorded. Use the following link to access it:https://ethz.zoom.us/rec/share/wPd3EpLNxkBITZXUr2H2au0wMIDEaaa8gSIY_KcOmEolghzOOdaSdAv7oyCjFQCc?startTime=1585220123000

The k-means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is a state-of-the-art algorithm for solving the k-means clustering problem and is known to give an O(log k)-approximation in expectation. Recently, Lattanzi and Sohler (ICML 2019) proposed augmenting k-means++ with O(k log log k) local search steps to yield a constant approximation (in expectation) to the k-means clustering problem. In this work, we improve their analysis to show that, for any arbitrarily small constant ε > 0, with only εk additional local search steps, one can achieve a constant approximation guarantee (with high probability in k), resolving an open problem in their paper.

Joint work with Davin Choo, Christoph Grunau, and Václav Rozhoň.

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