# The Quorum Deployment Problem

Quorum systems are commonly used to maintain the consistency of replicated data in adistributed system. Much research has been devoted to developing quorum systems with good theoreticalproperties, such as fault tolerance and high availability. However, even given a theoreticallygood quorum system, it is not obvious how to efficiently deploy such a system in a real network. Thispaper introduces a new combinatorial optimization problem, the Quorum Deployment Problem, andstudies its complexity. We demonstrate that it is NP-hard to approximate the Quorum DeploymentProblem 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 withmetric cost. We begin to study algorithms for variants of the problem. Some variants can be solved optimallyin polynomial time and some NP-hard variants can be approximated to within a constant factor.