Rati Gelashvili: Optimal Space Complexity of Consensus for Anonymous Processes

Tuesday, May 26, 2015 - 1:00pm to 2:30pm
Location: 
32-G631
Speaker: 
Rati Gelashvili
Biography: 
MIT

Abstract:
Optimal space complexity of consensus in shared memory is a decades-old open problem. For a system of $n$ processes, no algorithm is known that uses sublinear number of registers. However, the best known lower bound due to~\cite{FHS98} is $\Omega(\sqrt{n})$ registers.

The special symmetric case of the problem where processes are anonymous (run the same algorithm) has also attracted attention.
Even in this case, the best lower and upper bounds are still $\Omega(\sqrt{n})$ and $O(n)$. Moreover, the authors of~\cite{FHS98} first proved their lower bound for anonymous processes, and then extended it to the general case. As such, resolving the anonymous case might be a significant step towards understanding and solving the problem.

In this work, we show that in the system of anonymous processes, any consensus algorithm satisfying nondeterministic solo termination has to use $\Omega(n)$ read-write registers in some execution. This implies an $\Omega(n)$ lower bound on the space complexity of deterministic obstruction-free and randomized wait-free consensus, matching the upper bound and closes the symmetric case of the open problem.