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An Efficient Riemannian Gradient based Algorithm for Max-Cut Problems
  • Mohamad Mahdi Mohades ,
  • Mohammad Hossein Kahaei
Mohamad Mahdi Mohades
iran university of science and technology

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Mohammad Hossein Kahaei
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Abstract

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.
Mar 2022Published in IEEE Transactions on Circuits and Systems II: Express Briefs volume 69 issue 3 on pages 1882-1886. 10.1109/TCSII.2021.3104251