Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of counting the interior edge crossings when a bipartite graph G = (V, E) with node set V and edge set E is drawn such that the nodes of the two shores of the bipartition are drawn as distinct points on two parallel lines and the edges as straight line segments. The efficient solution of this problem is important in layered graph drawing. Our main observation is that it can be reduced to counting the inversions of a certain sequence. This leads to an O(|E|+|C|) algorithm, where C denotes the set of pairwise interior edge crossings, as ll as to a simple O(|E| log |Vsmall|) algorithm, where Vsmall is the smaller cardinality node set in the bipartition of the node set V of the graph.  present the algorithms and the results of computational experiments with these and other algorithms on a large collection of instances.
['Wilhelm Barth', 'Michael Jünger', 'Petra Mutzel']
I am writing a research paper on a idea Simple and Efficient Bilayer Cross Counting
[{"from": "human", "value": "I am writing a research paper on a idea Simple and Efficient Bilayer Cross Counting"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of counting the interior edge crossings when a bipartite graph G = (V, E) with node set V and edge set E is drawn such that the nodes of the two shores of the bipartition are drawn as distinct points on two parallel lines and the edges as straight line segments. The efficient solution of this problem is important in layered graph drawing. Our main observation is that it can be reduced to counting the inversions of a certain sequence. This leads to an O(|E|+|C|) algorithm, where C denotes the set of pairwise interior edge crossings, as ll as to a simple O(|E| log |Vsmall|) algorithm, where Vsmall is the smaller cardinality node set in the bipartition of the node set V of the graph.  present the algorithms and the results of computational experiments with these and other algorithms on a large collection of instances."}]