Fixed-parameter tractability of Venn diversity

Establish whether Venn diversity admits a fixed-parameter tractable algorithm in the general implicit set-system setting considered for the consistently diverse diversity measures.

Background

The paper develops an oracle-based fixed-parameter framework for diverse solutions under consistently diverse objectives, including Max-Sum Diversity, Max-Min Diversity, and Max-Coverage Diversity. The authors explicitly state that their techniques do not establish fixed-parameter tractability for Venn diversity and leave the question of whether such an algorithm exists in the general setting unresolved.