Grunau, Christoph
[VerfasserIn];
Özüdoğru, Ahmet Alper
[VerfasserIn];
Rozhoň, Václav
[VerfasserIn]
;
Christoph Grunau and Ahmet Alper Özüdoğru and Václav Rozhoň
[MitwirkendeR]
Anmerkungen:
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Beschreibung:
The k-means++ algorithm by Arthur and Vassilvitskii [SODA 2007] is a classical and time-tested algorithm for the k-means problem. While being very practical, the algorithm also has good theoretical guarantees: its solution is O(log k)-approximate, in expectation. In a recent work, Bhattacharya, Eube, Roglin, and Schmidt [ESA 2020] considered the following question: does the algorithm retain its guarantees if we allow for a slight adversarial noise in the sampling probability distributions used by the algorithm? This is motivated e.g. by the fact that computations with real numbers in k-means++ implementations are inexact. Surprisingly, the analysis under this scenario gets substantially more difficult and the authors were able to prove only a weaker approximation guarantee of O(log² k). In this paper, we close the gap by providing a tight, O(log k)-approximate guarantee for the k-means++ algorithm with noise.