Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Gomory and Hu proved that the  $\left{n\atop 2}\right$  maxflow problems in an undirected network have at most n-1 distinct solution values.  generalize their theorems in several ways. An interesting special case is that the On4 2-commodity maxflow problems on an undirected network have at most  $\left{n\atop 2}\right$  distinct solution values. These results follow from general theorems on the number of distinct solution values to sets of optimization problems.  then show how the solutions can be compactly represented by a basis of the solution matrix A, where aij = 1 if solution j is feasible for problem i, and aij = 0 otherwise. For the special case of the 2-cut problem  also show how to construct such a representation efficiently.
['Refael Hassin']
I am writing a research paper on a idea Solution Bases of Multiterminal Cut Problems
[{"from": "human", "value": "I am writing a research paper on a idea Solution Bases of Multiterminal Cut Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Gomory and Hu proved that the  $\\left{n\\atop 2}\\right$  maxflow problems in an undirected network have at most n-1 distinct solution values.  generalize their theorems in several ways. An interesting special case is that the On4 2-commodity maxflow problems on an undirected network have at most  $\\left{n\\atop 2}\\right$  distinct solution values. These results follow from general theorems on the number of distinct solution values to sets of optimization problems.  then show how the solutions can be compactly represented by a basis of the solution matrix A, where aij = 1 if solution j is feasible for problem i, and aij = 0 otherwise. For the special case of the 2-cut problem  also show how to construct such a representation efficiently."}]