Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The minimum rank problem asks to find the minimum rank over all matrices with a given pattern associated with a graph. This problem is NP-hard, and there is no known approximation method. Further, this problem has no straightforward convex relaxation. In this article, a numerical algorithm is given to heuristically approximate the minimum rank using alternating projections. The effectiveness of this algorithm is demonstrated by comparing its results to a related parameter: the zero-forcing number. Using these methods, numerical evidence for the minimum rank graph complement conjecture is provided.
['Franklin H. J. Kenter']
I am writing a research paper on a idea Approximating the minimum rank of a graph via alternating projection
[{"from": "human", "value": "I am writing a research paper on a idea Approximating the minimum rank of a graph via alternating projection"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The minimum rank problem asks to find the minimum rank over all matrices with a given pattern associated with a graph. This problem is NP-hard, and there is no known approximation method. Further, this problem has no straightforward convex relaxation. In this article, a numerical algorithm is given to heuristically approximate the minimum rank using alternating projections. The effectiveness of this algorithm is demonstrated by comparing its results to a related parameter: the zero-forcing number. Using these methods, numerical evidence for the minimum rank graph complement conjecture is provided."}]