Clustering with Fair-Center Representation

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

“…They established the polynomial-time inapproximability for the general variant with intersecting groups and presented polynomial-time approximation algorithms for the case with disjoint groups. In a subsequent work, Thejaswi et al [26] studied the variant with intersecting groups, offering complexity results and parameterized approximation algorithms for the diversity-aware k-median problem. This paper extends the work of Thejaswi et al [26], expanding the scope to include prevalent clustering formulations and extending the approach to accommodate both k-means and k-supplier objectives.…”

“…In a subsequent work, Thejaswi et al [26] studied the variant with intersecting groups, offering complexity results and parameterized approximation algorithms for the diversity-aware k-median problem. This paper extends the work of Thejaswi et al [26], expanding the scope to include prevalent clustering formulations and extending the approach to accommodate both k-means and k-supplier objectives. Additionally, we establish the optimality of presented algorithms based on standard complexity theory assumptions.…”

“…Recently, Thejaswi et al [25] introduced the diversity-aware k-median problem with lower-bound requirements on cluster centers from each group and overlapping facility groups. This increased level of generality increases the computational complexity of the problem, making it inapproximable in polynomial time and W[2]-hard with respect to parameter k. In a subsequent work, Thejaswi et al [26] present a parameterized approximation algorithm with respect to parameters k and t for diversity-aware k-median with 1 + 2 e + ǫ factor, where t is the number of groups. In this paper, we broaden our scope and introduce a generalized framework for solving diversityaware clustering with k-median, k-means, and k-supplier objectives, accommodating overlapping facility groups.…”

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

“…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.…”

“…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.…”