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Due to the recent cases of algorithmic bias in datadriven decision-making, machine learning methods are being put under the microscope in order to understand the root cause of these biases and how to correct them. Here, we consider a basic algorithmic task that is central in machine learning: subsampling from a large data set. Subsamples are used both as an end-goal in data summarization (where fairness could either be a legal, political or moral requirement) and to train algorithms (where biases in the samples are often a source of bias in the resulting model). Consequently, there is a growing effort to modify either the subsampling methods or the algorithms themselves in order to ensure fairness. However, in doing so, a question that seems to be overlooked is whether it is possible to produce fair subsamples that are also adequately representative of the feature space of the data set -an important and classic requirement in machine learning. Can diversity and fairness be simultaneously ensured? We start by noting that, in some applications, guaranteeing one does not necessarily guarantee the other, and a new approach is required. Subsequently, we present an algorithmic framework which allows us to produce both fair and diverse samples. Our experimental results on an image summarization task show marked improvements in fairness without compromising feature diversity by much, giving us the best of both the worlds.

Complex queries for massive data analysis jobs have become increasingly commonplace. Many such queries contain common subexpressions, either within a single query or among multiple queries submitted as a batch. Conventional query optimizers do not exploit these subexpressions and produce sub-optimal plans. The problem of multi-query optimization (MQO) is to generate an optimal combined evaluation plan by computing common subexpressions once and reusing them. Exhaustive algorithms for MQO explore an O(n n ) search space. Thus, this problem has primarily been tackled using various heuristic algorithms, without providing any theoretical guarantees on the quality of their solution.In this paper, instead of the conventional cost minimization problem, we treat the problem as maximizing a linear transformation of the cost function. We propose a greedy algorithm for this transformed formulation of the problem, which under weak, intuitive assumptions, provides an approximation factor guarantee for this formulation. We go on to show that this factor is optimal, unless P = NP. Another noteworthy point about our algorithm is that it can be easily incorporated into existing transformation-based optimizers. We finally propose optimizations which can be used to improve the efficiency of our algorithm.