Matrix representation and gradient flows for NP-hard problems |
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Authors: | W. S. Wong |
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Affiliation: | (1) Department of Information Engineering, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong |
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Abstract: | Over the past decade, a number of connections between continuous flows and numerical algorithms were established. Recently, Brockett and Wong reported a connection between gradient flows on the special orthogonal groupLO(n) and local search solutions for the assignment problem. In this paper, we describe a uniform formulation for certain NP-hard combinatorial optimization problems in matrix form and examine their connection with gradient flows onLO(n). For these problems, there is a correspondence between the so-called 2-opt solutions and asymptotically stable critical points of an associated gradient flow. |
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Keywords: | Gradient flows assignment problem traveling salesman problem graph partitioning problem local search |
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