Chained Index Ω(n) lower bound for large k (k = Ω(n/log n))

Determine whether any protocol that solves the Chained Index problem CI_{n,k} must use Ω(n) bits of total communication when k = Ω(n/log n) in the standard one-way blackboard model.

Background

The paper proves an Ω(n) lower bound for CI_{n,k} whenever k = o(n/log n), nearly settling a conjecture of Cormode et al. asserting Ω(n) communication for CI_{n,k}. The only remaining parameter regime not covered by the proof is when k is sufficiently large, specifically k = Ω(n/log n).

Resolving this remaining case would close the gap and fully settle the conjectured Ω(n) communication lower bound for CI_{n,k} across all k.