Minimum Vertex Augmentation

This paper introduces a class of graph problems named minimum vertex augmentation (MVA). Given an input graph 𝐺 where each vertex carries a binary color 0 or 1, we want to flip the colors of the fewest 0-vertices such that the subgraph induced by all the (original and new) 1-vertices satisfies a user-defined predicate 𝜋. In other words, the goal is to minimally augment the subset of 1-vertices to uphold the property 𝜋. Different formulations of 𝜋 instantiate the framework into concrete problems at the core of numerous applications. We first describe a suite of techniques for solving MVA problems with strong performance guarantees, and then present a generic algorithmic paradigm that a user can instantiate to deal with ad-hoc MVA problems. The effectiveness and efficiency of our solutions are verified with an extensive experimental evaluation.