Graph Normalization: A Fast Differentiable Solver for Maximum Weight Independent Set
Researchers have unveiled a novel approach known as Graph Normalization (GN), aimed at solving the challenging NP-hard Maximum Weight Independent Set (MWIS) problem. This problem intersects with various combinatorial areas, including scheduling and optimal assignment. Unlike traditional methods like Belief Propagation, GN guarantees convergence to a binary Maximum Independent Set. The technique employs an efficient quasi-Newton descent strategy through Majorization-Minimization, enhancing the relaxed primal objective. Additionally, GN shares a theoretical link with Replicator Dynamics from nonlinear evolutionary game theory, where vertices vie for positions within the independent set, reflecting principles from Fisher's Fundamental Theorem of Natural Selection.
Key facts
- Graph Normalization (GN) is a differentiable approximation engine for the NP-hard Maximum Weight Independent Set (MWIS) problem.
- MWIS includes optimal assignment, scheduling, set packing, and MAP inference in discrete Markov Random Fields.
- GN always converges to a binary indicator of a Maximum Independent Set, unlike Belief Propagation.
- GN uses a fast quasi-Newton descent via exact Majorization-Minimization step.
- GN is equivalent to Replicator Dynamics of a nonlinear evolutionary game.
- The GN game follows Fisher's Fundamental Theorem of Natural Selection.
- Average fitness equals the MWIS primal objective and strictly increases.
- The paper is published on arXiv with ID 2605.05330.
Entities
Institutions
- arXiv