Replica Placement for Availability in the Worst Case

We explore the problem of placing object replicas on nodes in a distributed system to maximize the number of objects that remain available when node failures occur. In our model, failing (the nodes hosting) a given threshold of replicas is sufficient to disable each object, and the adversary selects which nodes to fail to minimize the number of objects that remain available. We specifically explore placement strategies based on combinatorial structures called t-packings; provide a lower bound for the object availability they offer; show that these placements offer availability that is c-competitive with optimal; propose an efficient algorithm for computing combinations of t-packings that maximize their availability lower bound; and provide parameter selection strategies to concretely instantiate our schemes for different system sizes. We compare the availability offered by our approach to that of random replica placement, owing to the popularity of the latter approach in previous work. After quantifying the availability offered by random replica placement in our model, we show that our combinatorial strategy yields placements with better availability than random replica placement for many realistic parameter values.