The Linear-Array Conjecture in Communication Complexity is False

A linear array network consists of k + 1 processors P0; P1; : : : ; Pk with links only between Pi and Pi+1 0 i k. It is required to compute some boolean function f x; y in this network, where initially x is stored at P0 and y is stored at Pk. Let Dkf be the total number of bits that must be exchanged to compute f in worst case. Clearly, Dkf k Df , where Df is the standard two-party communication complexity of f . Tiwari proved that for almost all functions Dkf kDf ,O1 and conjectured that this is true for all functions. In this paper we disprove Tiwari's conjecture, by exhibiting an in nite family of functions for which Dkf is essentially at most 3 4k Df . Our construction also leads to progress on another major problem in this area: It is easy to bound the two-party communication complexity of any function, given the least number of monochromatic rectangles in any partition of the input space. How tight are such bounds? We exhibit certain functions, for which the two-pa...

• Type: Conference
• Year: 1996
• Where: STOC
• Authors: Eyal Kushilevitz, Nathan Linial, Rafail Ostrovsky
• Keywords: Algorithms, Linear Array Network, Standard Two-party Communication, STOC 1996, Two-party Communication Complexity