Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  unify several graph partitioning problems including multicut, multiway cut, and k-cut, into a single problem. The input to a requirement cut problem is an undirected edge-ighted graph G=(V,E), and g groups of vertices X1,⋯,Xg⊆V, each with a requirement ri beten 0 and |Xi|. The goal is to find a minimum cost set of edges whose removal separates each group Xi into at least ri disconnected components.#R##N##R##N# give an O(log n log (gR)) approximation algorithm for the requirement cut problem, where n is the total number of vertices, g is the number of groups, and R is the maximum requirement.  also show that the integrality gap of a natural LP relaxation for this problem is bounded by O(log n log (gR)). On trees,  obtain an improved guarantee of O(log (gR)). There is a natural Ω (log g) hardness of approximation for the requirement cut problem.
['Viswanath Nagarajan', 'R. Ravi']
I am writing a research paper on a idea Approximation algorithms for requirement cut on graphs
[{"from": "human", "value": "I am writing a research paper on a idea Approximation algorithms for requirement cut on graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  unify several graph partitioning problems including multicut, multiway cut, and k-cut, into a single problem. The input to a requirement cut problem is an undirected edge-ighted graph G=(V,E), and g groups of vertices X1,\u22ef,Xg\u2286V, each with a requirement ri beten 0 and |Xi|. The goal is to find a minimum cost set of edges whose removal separates each group Xi into at least ri disconnected components.#R##N##R##N# give an O(log n log (gR)) approximation algorithm for the requirement cut problem, where n is the total number of vertices, g is the number of groups, and R is the maximum requirement.  also show that the integrality gap of a natural LP relaxation for this problem is bounded by O(log n log (gR)). On trees,  obtain an improved guarantee of O(log (gR)). There is a natural \u03a9 (log g) hardness of approximation for the requirement cut problem."}]