Locally Balanced Allocations Under Strong Byzantine Influence.

The Power of Two Choices (PoTC) is a commonly used technique to balance the incoming load (balls) into available resources (bins) – for each coming ball, two bins are selected uniformly at random and the one with smaller number of balls is chosen as the location of the current ball. We study a generalization of PoTC to a fault-prone setting – faulty bin(s) could present malicious information to enforce allocation decision on any of the two bins. Given m balls and n bins, such that no more than f of the bins are faulty, we show that the maximum loaded honest bin receives a surplus of a logarithmic number of balls with respect to f . Our result generalizes the classic bounds of the Power of Two Choices in the presence of a strong Byzantine adversary. Our solution and methods of analysis can help to efficiently implement and analyze resilient online local decisions made by processes when solving fundamental problems that depend on load balancing under the presence of Byzantine failures.