Diversity-Aware k-median: Clustering with Fair Center Representation

Abstract

Shetty and Sohan Shetty. Even though I have not managed to keep in regular contact with all of you because of the geographical distance, I really miss you all. I thank my family for their support over the years and I am forever indebt of my mother's unconditional love. Finally, Heli thank you for your existence in my life.

Independent Set in k-Claw-Free Graphs: Conditional $$\chi $$-Boundedness and the Power of LP/SDP Relaxations

“…In Publication III, we consider a notion of fairness for the centers in the solution. This problem, introduced by [122], is called Diversity-aware Clustering, and the goal is choose k centers to minimize certain objective while avoiding under-representation and over-representation of communities defined over the facility set F. This problem naturally arises, among many others, in the context of committee selection, where the goal is to form a committee that is not only easily accessible (in terms of distances) but is also as diverse as possible. Now, let us define a special case of this problem, which will be of interest in this section.…”

“…In terms of the algorithmic framework, it would be fascinating to extend it to clustering objectives that go beyond norms. For instance, many objectives impose specific constraints on how points are assigned to open centers, such as capacity [6,61,50], different notions of fairness [21,46,45], and diversity constraints [97,122,121]. These extensions present exciting opportunities for future investigation.…”

“…In clustering, there are at least 10 notions of fairness (see [1] for a survey and references therein). For example, [122] considers fairness in the facilities opened by avoiding under-representation and over-representation of communities (this is the topic of our next chapter).…”

“…This chapter is based on Publication III [121] and studies another variant of fair clustering, called diversity-aware clustering [123], that ensures diversity amongst the selected clustering centers. Although most of our results extend to other classical clustering problems, we limit our attention to diversity-aware formulations of k-MEDIAN and k-MEANS.…”

“…Even though diversity-aware formulations of the clustering problems are very recent [123], a limited variation [77], studied under the context of content distribution network application, has been known for a decade. This problem, known as RED-BLUE MEDIAN, is defined when we have two disjoint groups and each group has only an upper-bound requirement.…”