Practical Graph Bipartization with Applications in Near-Term Quantum Computing
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Abstract
We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal), motivated by recent advances in near-term quantum computing hardware and the related embedding problems. We assemble a preprocessing suite of fast input reduction routines from the odd cycle transversal and vertex cover literature, allowing the slower branching algorithms to be compared on identically-preprocessed data. In addition to combinatorial branching algorithms, we also study multiple methods for computing graph bipartization with integer linear programming solvers. Evaluating the practical performance of these algorithm, two use cases in quantum annealing are studied with a quadratic unconstrained binary optimization problem corpus. Finally, we provide all code and data in an open source suite, including a Python API for accessing reduction routines and branching algorithms, along with scripts for fully replicating our results.