Date of Award
Department of Computer Science
We study the communication complexity of the SHIFT (equivalently, SUM-INDEX) function in a 3-party simultaneous message model. Alice and Bob share an n-bit string x and Alice holds an index i and Bob an index j. They must send messages to a referee who knows only n, i and j, enabling him to determine x[(i+j) mod n]. Surprisingly, it is possible to achieve nontrivial savings even with such a strong restriction: Bob can now make do with only ceil(n/2) bits. Here we show that this bound is completely tight, for all n. This is an exact lower bound, with no asymptotics involved.
Adelfio, Marco D., "Lower Bounds on the Communication Complexity of Shifting" (2005). Dartmouth College Undergraduate Theses. 47.