Lower Bounds on the Multiparty Communication Complexity

Pavol Ďuriš, José D.P. Rolim
1998 Journal of computer and system sciences (Print)  
We derive a general technique for obtaining lower bounds on the multiparty communication complexity of boolean functions. We extend the two-party method based on a crossing sequence argument introduced by Yao to the multiparty communication model. We use our technique to derive optimal lower and upper bounds of some simple boolean functions. Lower bounds for the multiparty model have been a challenge since (D. Dolev and T. Feder, in"Proceedings, 30th IEEE FOCS, 1989," pp. 428 433), where only
more » ... upper bound on the number of bits exchanged by a deterministic algorithm computing a boolean function f (x 1 , ..., x n ) was derived, namely of the order (k 0 C 0 )(k 1 C 1 ) 2 , up to logarithmic factors, where k 1 and C 1 are the number of processors accessed and the bits exchanged in a nondeterministic algorithm for f, and k 0 and C 0 are the analogous parameters for the complementary function 1& f. We show that C 0 n(1+2 C1 ) and D n(1+2 C1 ), where D is the number of bits exchanged by a deterministic algorithm computing f. We also investigate the power of a restricted multiparty communication model in which the coordinator is allowed to send at most one message to each party. ]
doi:10.1006/jcss.1997.1547 fatcat:ugcyqaftrzekpidhiyhsy6pwie