Learning to Find Hard Instances of Graph Problems

Finding hard instances, which need a long time to solve, of graph problems such as the graph coloring problem and the maximum clique problem, is important for (1) building a good benchmark for evaluating the performance of algorithms, and (2) analyzing the algorithms to accelerate them. The existing methods for generating hard instances rely on parameters or rules that are found by domain experts; however, they are specific to the problem. Hence, it is difficult to generate hard instances for general cases. To address this issue, in this paper, we formulate finding hard instances of graph problems as two equivalent optimization problems. Then, we propose a method to automatically find hard instances by solving the optimization problems. The advantage of the proposed algorithm over the existing rule based approach is that it does not require any task specific knowledge. To the best of our knowledge, this is the first non-trivial method in the literature to automatically find hard instances. Through experiments on various problems, we demonstrate that our proposed method can generate instances that are a few to several orders of magnitude harder than the random based approach in many settings. In particular, our method outperforms rule-based algorithms in the 3-coloring problem.