A result of Johnson and Lindenstrauss [13] shows that a set of n points in high dimensional Euclidean space can be mapped into an O(log n/ϵ2)‐dimensional Euclidean space such that the distance… Expand

This paper presents the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity, an intuitive diminishing returns property, and proves that better approximation algorithms do not exist unless NP-complete problems admit efficient algorithms.Expand

This work considers both general doubling metrics, as well as more restricted families such as those arising from trees, from graphs excluding a fixed minor, and from snowflaked metrics, which contains many families of metrics that occur in applied settings.Expand

This work establishes a relation between this collection of network design problems and a variant of the facility location problem introduced by Karger and Minkoff, and provides optimal and approximate algorithms for several variants of this problem, depending on whether the traffic matrix is required to be symmetric.Expand

The Johnson-Lindenstrauss lemma shows that a set of n points in high dimensional Euclidean space can be mapped down into an O(log n== 2) dimensional Euclidean space such that the distance between any… Expand

A new algorithm is presented whose regret is nearly optimal, substantially improving upon previous work and can tolerate a significant amount of corruption with virtually no degradation in performance.Expand

These ideas are extended to give a simple greedy-based constant factor algorithms for non-monotone submodular maximization subject to a knapsack constraint, and for (online) secretary setting subject to uniform matroid or a partition matroid constraint.Expand

A simple and easy-to-analyze randomized approximation algorithms for several well-studied NP-hard network design problems and a simple constant-factor approximation algorithm for the single-sink buy-at-bulk network design problem.Expand

If any c-approximation to the given clustering objective φ is e-close to the target, then this paper shows that this guarantee can be achieved for any constant c > 1, and for the min-sum objective the authors can do this for any Constant c > 2.Expand

It is shown that many such problems indeed have good approximation algorithms that preserve differential privacy, even in cases where it is impossible to preserve cryptographic definitions of privacy while computing any non-trivial approximation to even the value of an optimal solution, let alone the entire solution.Expand