Efficient Graph-Based Resource Allocation Scheme Using Maximal Independent Set for Randomly- Deployed Small Star Networks

Using synchronized oscillators to compute the maximum independent set

Not all computing problems are created equal. The inherent complexity of processing certain classes of problems using digital computers has inspired the exploration of alternate computing paradigms. Coupled oscillators exhibiting rich spatio-temporal dynamics have been proposed for solving hard optimization problems. However, the physical implementation of such systems has been constrained to small prototypes. Consequently, the computational properties of this paradigm remain inadequately explored. Here, we demonstrate an integrated circuit of thirty oscillators with highly reconfigurable coupling to compute optimal/near-optimal solutions to the archetypally hard Maximum Independent Set problem with over 90% accuracy. This platform uniquely enables us to characterize the dynamical and computational properties of this hardware approach. We show that the Maximum Independent Set is more challenging to compute in sparser graphs than in denser ones. Finally, using simulations we evaluate the scalability of the proposed approach. Our work marks an important step towards enabling application-specific analog computing platforms to solve computationally hard problems.

Designing efficient analog dynamical systems for solving hard optimization problems remains a challenge. Here, the authors demonstrate a dynamical system of thirty oscillators with reconfigurable coupling to compute optimal/near-optimal solutions to the hard Maximum Independent Set problem with over 90% accuracy.