On the Communication-Computation Tradeoff for Symmetric Private Linear Computation

We consider the problem of symmetric private linear computation (SPLC) over a replicated storage system with colluding and straggler constraints. The SPLC problem allows the user to privately compute a linear combination of multiple files from a set of replicated servers, even in the presence of straggler servers that can bottleneck the entire computation. It is guaranteed that a certain number of colluding servers learn nothing about the coefficients of the linear combination, and the user must not learn any information about the files other than the desired linear computation. Unlike previous private computation literature that mainly focused on decreasing download cost from servers, we aim to establish a flexible tradeoff between communication costs and computational complexities. In particular, we propose a novel SPLC scheme under the assumption of a fixed number of stragglers. Additionally, by generalizing this SPLC scheme, we construct an adaptive SPLC scheme capable of tolerating the presence of a varying number of stragglers, even if their identities and numbers are unknown in advance. Compared to the SPLC scheme with a fixed number of stragglers, the adaptive SPLC scheme achieves a lower communication cost based on the actual number of stragglers, albeit at the cost of increased computational complexities. Both types of SPLC schemes achieve flexible performance tradeoffs and can be employed to optimize system efficiency in practice.