Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate multidimensional covering mechanism-design problems, wherein there are m items that need to be covered and n agents who provide covering objects, with each agent i having a private cost for the covering objects he provides. The goal is to select a set of covering objects of minimum total cost that together cover all the items.#R##N##R##N# focus on two representative covering problems: uncapacitated facility location (UFL) and vertex cover (VC). For multidimensional UFL,  give a black-box method to transform any Lagrangian-multiplier-preservingρ-approximation algorithm for UFL to a truthful-in-expectation, ρ-approx. mechanism. This yields the first result for multidimensional UFL, namely a truthful-in-expectation 2-approximation mechanism.#R##N##R##N#For multidimensional VC (Multi-VC),  develop a decomposition method that reduces the mechanism-design problem into the simpler task of constructing threshold mechanisms, which are a restricted class of truthful mechanisms, for simpler (in terms of graph structure or problem dimension) instances of Multi-VC. By suitably designing the decomposition and the threshold mechanisms it uses as building blocks,  obtain truthful mechanisms with approximation ratios (n is the number of nodes): (1) O(logn) for Multi-VC on any minor-closed family of graphs; and (2) O(r2logn) for r-dimensional VC on any graph. These are the first truthful mechanisms for Multi-VC with non-trivial approximation guarantees.
['Hadi Minooei', 'Chaitanya Swamy']
I am writing a research paper on a idea Truthful mechanism design for multidimensional covering problems
[{"from": "human", "value": "I am writing a research paper on a idea Truthful mechanism design for multidimensional covering problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate multidimensional covering mechanism-design problems, wherein there are m items that need to be covered and n agents who provide covering objects, with each agent i having a private cost for the covering objects he provides. The goal is to select a set of covering objects of minimum total cost that together cover all the items.#R##N##R##N# focus on two representative covering problems: uncapacitated facility location (UFL) and vertex cover (VC). For multidimensional UFL,  give a black-box method to transform any Lagrangian-multiplier-preserving\u03c1-approximation algorithm for UFL to a truthful-in-expectation, \u03c1-approx. mechanism. This yields the first result for multidimensional UFL, namely a truthful-in-expectation 2-approximation mechanism.#R##N##R##N#For multidimensional VC (Multi-VC),  develop a decomposition method that reduces the mechanism-design problem into the simpler task of constructing threshold mechanisms, which are a restricted class of truthful mechanisms, for simpler (in terms of graph structure or problem dimension) instances of Multi-VC. By suitably designing the decomposition and the threshold mechanisms it uses as building blocks,  obtain truthful mechanisms with approximation ratios (n is the number of nodes): (1) O(logn) for Multi-VC on any minor-closed family of graphs; and (2) O(r2logn) for r-dimensional VC on any graph. These are the first truthful mechanisms for Multi-VC with non-trivial approximation guarantees."}]