NN-Baker: A Neural-network Infused Algorithmic Framework for Optimization Problems on Geometric Intersection Graphs

Recent years have witnessed a surge of approaches to use neural networks to help tackle combinatorial optimization problems, including graph optimization problems. However, theoretical understanding of such approaches remains limited. In this paper, we consider the geometric setting, where graphs are induced by points in a fixed dimensional Euclidean space. We show that several graph optimization problems can be approximated by an algorithm that is polynomial in graph size n via a framework we propose, call the Baker-paradigm. More importantly, a key advantage of the Baker-paradigm is that it decomposes the input problem into (at most linear number of) small sub-problems of fixed sizes (independent of the size of the input).