Optimally reconnecting weighted graphs against an edge-destroying adversary

Abstract: We introduce a model involving two adversaries Buster and Fixer taking turns modifying a connected graph, where each round consists of Buster deleting a subset of edges and Fixer responding by adding edges from a reserve set of weighted edges to leave the graph connected. With the weights representing the cost for Fixer to use specific reserve edges to reconnect the graph, we provide a reasonable definition for what should constitute an optimal strategy for Fixer to keep the graph connected for as long as possible as cheaply as possible, and prove that a greedy strategy for Fixer satisfies our conditions for optimality.