Date of Award


Document Type

Thesis (Undergraduate)


Department of Computer Science

First Advisor

Amit Chakrabarti


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.


Originally posted in the Dartmouth College Computer Science Technical Report Series, number TR2005-548.