There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of a budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node. To further facilitate the combinatorial nature of the problem, GCOMB utilizes a Q-learning framework, which is made efficient through importance sampling. We perform extensive experiments on real graphs to benchmark the efficiency and efficacy of GCOMB. Our results establish that GCOMB is 100 times faster and marginally better in quality than state-of-the-art algorithms for learning combinatorial algorithms. Additionally, a case-study on the practical combinatorial problem of Influence Maximization (IM) shows GCOMB is 150 times faster than the specialized IM algorithm IMM with similar quality.

High static power dissipation is one of the largest hurdles in the widespread adoption of on-chip optical networks. There are numerous proposals in literature for the reduction of static power by predicting the activity in future time intervals, and then powering off the laser, and also by sharing optical bandwidth. We propose a novel scheme called ColdBus in this paper that introduces a new method of predicting the optical NoC traffic using program counter addresses, moreover, we then propose novel structures and predictors for handling mispredictions. These units allow optical transmitters to share bandwidth between them while simultaneously minimizing static power. We show that ColdBus consumes 4.1X less optical power than other state of the art proposals. It additionally has a speedup of 3.1%, and improves ED2 by 18% for a suite of Splash, Parsec, and Parboil benchmarks.