Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Stackelberg Minimum Spanning Tree Game (StackMST) is defined in terms of a graph G = (V, B ∪ R), with two disjoint sets of edges, blue B and red R, and costs {c e ≥ 0 : e ∈ R} defined for the red edges. Once the leader of the game defines prices {p e : e ∈ B} to the blue edges, the follor chooses a minimum ight spanning tree (V, E T), at cost e∈B∩E T p e + e∈R∩E T c e. The goal is to find prices to maximize the revenue e∈B∩E T p e collected by the leader.  introduce a reformulation and a Branch-and-cut-and-price algorithm for StackMST. The reformulation is obtained after applying KKT optimality conditions to a StackMST non-compact Bilevel Linear Programming formulation and is strengthened with a partial rank-1 RLT and with valid inequalities from the literature.  also implemented a Branch-and-cut algorithm for an extended formulation derived from another in the literature. A preliminary computational study comparing both methods is also presented.
['Vinicius Morais', 'Alexandre Salles da Cunha', 'Philippe Mahey']
I am writing a research paper on a idea A Branch-and-cut-and-price algorithm for the Stackelberg Minimum Spanning Tree Game
[{"from": "human", "value": "I am writing a research paper on a idea A Branch-and-cut-and-price algorithm for the Stackelberg Minimum Spanning Tree Game"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Stackelberg Minimum Spanning Tree Game (StackMST) is defined in terms of a graph G = (V, B \u222a R), with two disjoint sets of edges, blue B and red R, and costs {c e \u2265 0 : e \u2208 R} defined for the red edges. Once the leader of the game defines prices {p e : e \u2208 B} to the blue edges, the follor chooses a minimum ight spanning tree (V, E T), at cost e\u2208B\u2229E T p e + e\u2208R\u2229E T c e. The goal is to find prices to maximize the revenue e\u2208B\u2229E T p e collected by the leader.  introduce a reformulation and a Branch-and-cut-and-price algorithm for StackMST. The reformulation is obtained after applying KKT optimality conditions to a StackMST non-compact Bilevel Linear Programming formulation and is strengthened with a partial rank-1 RLT and with valid inequalities from the literature.  also implemented a Branch-and-cut algorithm for an extended formulation derived from another in the literature. A preliminary computational study comparing both methods is also presented."}]