Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Budget feasible mechanisms, recently initiated by Singer (FOCS 2010), extend algorithmic mechanism design problems to a realistic setting with a budget constraint.  consider the problem of designing truthful budget feasible mechanisms for monotone submodular functions:  give a randomized mechanism with an approximation ratio of 7.91 (improving on the previous best-known result 233.83), and a deterministic mechanism with an approximation ratio of 8.34.  also study the knapsack problem, which is a special submodular function, give a 2 + √2 approximation deterministic mechanism (improving on the previous best-known result 5), and a 3 approximation randomized mechanism.  provide similar results for an extended knapsack problem with heterogeneous items, where items are divided into groups and one can pick at most one item from each group.   Finally  show a lor bound of 1 + √2 for the approximation ratio of deterministic mechanisms and 2 for randomized mechanisms for knapsack, as ll as the general monotone submodular functions. Our lor bounds are unconditional, and do not rely on any computational or complexity assumptions.
['Ning Chen', 'Nick Gravin', 'Pinyan Lu']
I am writing a research paper on a idea On the approximability of budget feasible mechanisms
[{"from": "human", "value": "I am writing a research paper on a idea On the approximability of budget feasible mechanisms"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Budget feasible mechanisms, recently initiated by Singer (FOCS 2010), extend algorithmic mechanism design problems to a realistic setting with a budget constraint.  consider the problem of designing truthful budget feasible mechanisms for monotone submodular functions:  give a randomized mechanism with an approximation ratio of 7.91 (improving on the previous best-known result 233.83), and a deterministic mechanism with an approximation ratio of 8.34.  also study the knapsack problem, which is a special submodular function, give a 2 + \u221a2 approximation deterministic mechanism (improving on the previous best-known result 5), and a 3 approximation randomized mechanism.  provide similar results for an extended knapsack problem with heterogeneous items, where items are divided into groups and one can pick at most one item from each group.   Finally  show a lor bound of 1 + \u221a2 for the approximation ratio of deterministic mechanisms and 2 for randomized mechanisms for knapsack, as ll as the general monotone submodular functions. Our lor bounds are unconditional, and do not rely on any computational or complexity assumptions."}]