Hellinger Strikes Back: A Note on the Multi-party Information Complexity of AND

The AND problem on t bits is a promise decision problem where either at most one bit of the input is set to 1 (NO instance) or all t bits are set to 1 (YES instance). In this note, I will give a new proof of an Ω(1/t ) lower bound on the information complexity of AND in the number-in-hand model of communication. This was recently established by Gronemeier, STACS 2009. The proof exploits the information geometry of communication protocols via Hellinger distance in a novel manner and avoids the analytic approach inherent in previous work. As previously known, this bound implies an Ω(n/t ) lower bound on the communication complexity of multiparty disjointness and consequently a Ω(n1−2/k ) space lower bound on estimating the k-th frequency moment Fk .

• Type: Conference
• Year: 2009
• Where: APPROX
• Authors: T. S. Jayram
• Keywords: Algorithms, APPROX 2009, Lower Bound, Promise Decision Problem, Space Lower Bound