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We study (Euclidean) $k$-median and $k$-means with constraints in thestreaming model.  There have been recent efforts to design unified algorithms to solveconstrained $k$-means problems without using knowledge of the specificconstraint at hand aside from mild assumptions like the polynomialcomputability of feasibility under the constraint (compute if a clusteringsatisfies the constraint) or the presence of an efficient assignment oracle(given a set of centers, produce an optimal assignment of points to the centerswhich satisfies the constraint). These algorithms have a running timeexponential in $k$, but can be applied to a wide range of constraints.  We demonstrate that a technique proposed in 2019 for solving a specificconstrained streaming $k$-means problem, namely fair $k$-means clustering,actually implies streaming algorithms for all these constraints. These work forlow dimensional Euclidean space. [Note that there are more algorithms forstreaming fair $k$-means today, in particular they exist for high dimensionalspaces now as well.]

Coresets for constrained k-median and k-means clustering in low dimensional Euclidean space