The Quorum Deployment Problem (Extended Abstract)

Quorum systems are commonly used to maintain the con- sistency of replicated data in a distributed system. Much research has been devoted to developing quorum systems with good theoretical prop- erties, such as fault tolerance and high availability. However, even given a theoretically good quorum system, it is not obvious how to e-ciently deploy such a system in a real network. This paper introduces a new combinatorial optimization problem, the Quorum Deployment Problem, and studies its complexity. We demonstrate that it is NP-hard to approx- imate the Quorum Deployment Problem within any factor of n-, where n is the number of nodes in the distributed network and - > 0. The problem is NP-hard in even the simplest possible distributed network: a one-dimensional line with metric cost. We begin to study algorithms for variants of the problem. Some variants can be solved optimally in poly- nomial time and some NP-hard variants can be approximated to within a constant factor.