Near-Optimal Lower Bounds on the Multi-Party Communication Complexity of Set Disjointness

We study the communication complexity of the set disjointness problem in the general multi-party model. For t players, each holding a subset of a universe of size n, we establish a near-optimal lower bound of Ω(n/(t log t)) on the communication complexity of the problem of determining whether their sets are disjoint. In the more restrictive one-way communication model, in which the players are required to speak in a predetermined order, we improve our bound to an optimal Ω(n/t). These results improve upon the earlier bounds of Ω(n/t2) in the general model, and Ω(ε2n/t1+ε) in the one-way model, due to Bar-Yossef, Jayram, Kumar, and Sivakumar [5]. As in the case of earlier results, our bounds apply to the unique intersection promise problem. This communication problem is known to have connections with the space complexity of approximating frequency moments in the data stream model. Our results lead to an improved space complexity lower bound of Ω(n1−2/k/ log n) for approxi...

• Type: Conference
• Year: 2003
• Where: COCO
• Authors: Amit Chakrabarti, Subhash Khot, Xiaodong Sun
• Keywords: COCO 2003, Communication Complexity, Lower Bound, Space Complexity