We present a learning-based approach to computing solutions for certain
NP-hard problems. Our approach combines deep learning techniques with useful
algorithmic elements from classic heuristics. The central component is a graph
convolutional network that is trained to estimate the likelihood, for each
vertex in a graph, of whether this vertex is part of the optimal solution. The
network is designed and trained to synthesize a diverse set of solutions, which
enables rapid exploration of the solution space via tree search. The presented
approach is evaluated on four canonical NP-hard problems and five datasets,
which include benchmark satisfiability problems and real social network graphs
with up to a hundred thousand nodes. Experimental results demonstrate that the
presented approach substantially outperforms recent deep learning work, and
performs on par with highly optimized state-of-the-art heuristic solvers for
some NP-hard problems. Experiments indicate that our approach generalizes
across datasets, and scales to graphs that are orders of magnitude larger than
those used during training.

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