Graph partitioning aims to divide a graph into $k$ disjoint subsets while optimizing a specific partitioning objective. The majority of formulations related to graph partitioning exhibit NP-hardness due to their combinatorial nature. As a result, conventional approximation algorithms rely on heuristic methods, sometimes with approximation guarantees and sometimes without. Unfortunately, traditional approaches are tailored for specific partitioning objectives and do not generalize well across other known partitioning objectives from the literature. To overcome this limitation, and learn heuristics from the data directly, neural approaches have emerged, demonstrating promising outcomes. In this study, we extend this line of work through a novel framework, NeuroCut. NeuroCut introduces two key innovations over prevailing methodologies. First, it is inductive to both graph topology and the partition count, which is provided at query time. Second, by leveraging a reinforcement learning based framework over node representations derived from a graph neural network, NeuroCut can accommodate any optimization objective, even those encompassing non-differentiable functions. Through empirical evaluation, we demonstrate that NeuroCut excels in identifying high-quality partitions, showcases strong generalization across a wide spectrum of partitioning objectives, and exhibits resilience to topological modifications.

Packet classification is a fundamental problem in computer networking. This problem exposes a hard tradeoff between the computation and state complexity, which makes it particularly challenging. To navigate this tradeoff, existing solutions rely on complex hand-tuned heuristics, which are brittle and hard to optimize. In this paper, we propose a deep reinforcement learning (RL) approach to solve the packet classification problem. There are several characteristics that make this problem a good fit for Deep RL. First, many of the existing solutions are iteratively building a decision tree by splitting nodes in the tree. Second, the effects of these actions (e.g., splitting nodes) can only be evaluated once we are done with building the tree. These two characteristics are naturally captured by the ability of RL to take actions that have sparse and delayed rewards. Third, it is computationally efficient to generate data traces and evaluate decision trees, which alleviate the notoriously high sample complexity problem of Deep RL algorithms. Our solution, NeuroCuts, uses succinct representations to encode state and action space, and efficiently explore candidate decision trees to optimize for a global objective. It produces compact decision trees optimized for a specific set of rules and a given performance metric, such as classification time, memory footprint, or a combination of the two. Evaluation on ClassBench shows that NeuroCuts outperforms existing hand-crafted algorithms in classification time by 18% at the median, and reduces both time and memory footprint by up to 3x.