Preparing for Disaster: Leveraging Precomputation to Efficiently Repair Graph Structures Upon Failures

Distributed algorithms for constructing structures such as a maximal independent set (MIS) or maximal matching (MM) are well-studied in standard message-passing network models. In this paper, we consider a natural variant of this problem in which we begin with an instance of the graph structure and partition our algorithm execution that follows into two stages. During the first stage after the graph structure is calculated, some additional precomputation is done. In the second stage, an arbitrary collection of k nodes are crashed. The goal is to then repair the structure as efficiently as possible. We are interested in the circumstances under which the repair can be faster than the time required to build the structure from scratch, and focus, in particular, on trade-offs in which extra precomputation rounds during the first stage can be traded for faster repairs during the second.