Constant-factor guarantees under departures and general shuffle schemes

Establish constant-factor approximation guarantees for the proposed dynamic coded distributed computing scheme under arbitrary feasible worker-disconnection patterns and for general coded distributed computing shuffle schemes beyond the class of instantly decodable XOR schemes.

Background

The paper develops a dynamic coded distributed computing scheme for MapReduce systems in which workers may depart and new clusters may join while the caches of surviving workers remain unchanged. Its Cartesian-product placement and delivery-aware Reduce-function reassignment yield an exact communication load for arbitrary feasible disconnection sets.

For the no-disconnection setting, the paper proves factors of two with arrivals and four without arrivals relative to the best instantly decodable XOR scheme over all feasible uncoded placements. The conclusion explicitly identifies the extension of constant-factor guarantees to arbitrary feasible disconnection patterns and to general coded distributed computing shuffle schemes as unresolved.