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An Efficient Riemannian Gradient based Algorithm for Max-Cut Problems

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posted on 03.02.2021, 02:16 by Mohamad Mahdi Mohades, Mohammad Hossein Kahaei

The max-cut problem addresses the problem of finding a cut for a graph that splits the graph into two subsets of vertices so that the number of edges between these two subsets is as large as possible. However, this problem is NP-Hard, which may be solved by suboptimal algorithms. In this paper, we propose a fast and accurate Riemannian optimization algorithm for solving the max-cut problem. To do so, we develop a gradient descent algorithm and prove its convergence. Our simulation results show that the proposed method is extremely efficient on some already-investigated graphs. Specifically, our method is on average 50 times faster than the best well-known techniques with slightly losing the performance, which is on average 0.9729 of the max-cut value of the others.

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Email Address of Submitting Author

mohamad_mohaddes@elec.iust.ac.ir

Submitting Author's Institution

iran university of science and technology

Submitting Author's Country

Iran

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