WeaveNet for Approximating Assignment Problems

Assignment, a task to match a limited number of elements, is a fundamental problem in informatics. Many assignment problems have no exact solvers due to their NP-hardness or incomplete input, and their approximation algorithms have been studied for a long time. However, individual practical applications have various objective functions and prior assumptions, which usually differ from academic studies. This gap hinders applying the algorithms to real problems despite their theoretically ensured performance. In contrast, a learning-based method can be a promising solution to fill the gap. To open a new vista for real-world assignment problems, we propose a novel neural network architecture, WeaveNet. Its core module, feature weaving layer, is stacked to model frequent communication between elements in a parameter-efficient way for solving the combinatorial problem of assignment. To evaluate the model, we approximated one of the most popular non-linear assignment problems, stable matching with two different strongly NP-hard settings. The experimental results showed its impressive performance among the learning-based baselines. Furthermore, we achieved better or comparative performance to the state-of-the-art algorithmic method, depending on the size of problem instances.