Theoretical Analysis of the $k$-Means Algorithm - A Survey
  The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to improve the algorithm. In this paper we survey the recent results in this direction as well as several extension of the basic $k$-means method. 
Johannes Bl\"omer, Christiane Lammersen, Melanie Schmidt, Christian   Sohler
cs.DS cs.LG