Communication-Space Tradeoffs for Unrestricted Protocols
Paul W. Beame, Martin Tompa, Peiyuan Yan · SIAM Journal on Computing · 1994
This paper introduces communicating branching programs and develops a general technique for demonstrating communication-space tradeoffs for pairs of communicating branching programs. This technique is then used to prove communication-space tradeoffs for any pair of communicating branching programs that hashes according to a universal family of hash functions. Other tradeoffs follow from this result. As an example, any pair of communicating Boolean branching programs that computes matrix-vector products over ${\text{GF}}(2)$ requires communication-space product $\Omega (n^2 )$, provided the space used is $o({n / {\log n}})$. These are the first examples of communication-space tradeoffs on a completely general model of communicating processes.