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``Composable core-sets'' are an efficient framework for solving optimizationproblems in massive data models. In this work, we consider efficientconstruction of composable core-sets for the determinant maximization problem.This can also be cast as the MAP inference task for determinantal pointprocesses, that have recently gained a lot of interest for modeling diversityand fairness. The problem was recently studied in [IMOR'18], where theydesigned composable core-sets with the optimal approximation bound of $\tildeO(k)^k$. On the other hand, the more practical Greedy algorithm has beenpreviously used in similar contexts. In this work, first we provide atheoretical approximation guarantee of $O(C^{k^2})$ for the Greedy algorithm inthe context of composable core-sets; Further, we propose to use a Local Searchbased algorithm that while being still practical, achieves a nearly optimalapproximation bound of $O(k)^{2k}$; Finally, we implement all three algorithmsand show the effectiveness of our proposed algorithm on standard data sets.

Composable Core-sets for Determinant Maximization: A Simple Near-Optimal Algorithm