2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1984)
Singer Island, FL
Oct. 24, 1984 to Oct. 26, 1984
P. Tiwari , University of Illinois at Urbana-Champaign
We prove that for almost all boolean functions f , the conmunication complexity of f on a linear array with p+1 processors is approximately p times its commuication complexity on a system with two processors. We use this result to develop a technique for establishing lower bounds on communication complexity on general networks by simulating them on linear arrays. Using this technique, we derive optimal lower bounds for ranking, distinctness, uniqueness and triangle-detection problems on the ring. The application of this technique to meshes and trees yields nontrivial near optimal lower bounds on the communicaton complexity of ranking and distinctness problems on these networks.
P. Tiwari, "Lower Bounds On Communication Complexity In Distributed Computer Networks", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 109-117, 1984, doi:10.1109/SFCS.1984.715907