Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of online scheduling of jobs on unrelated machines with dynamic speed scaling to minimize the sum of energy and ighted flow time.  give an algorithm with an almost optimal competitive ratio for arbitrary por functions. (No earlier results handled arbitrary por functions for minimizing flow time plus energy with unrelated machines.) For por functions of the form f(s) = sα for some constant α > 1,  get a competitive ratio of O(α/log α), improving upon a previous competitive ratio of O(α2) by Anand et al. [3], along with a matching lor bound of Ω(α/log α). Further, in the resource augmentation model, with a 1 + e speed up,  give a 2(1/e + 1) competitive algorithm, with essentially the same techniques, improving the bound of 1 + O(1/e2) by Gupta et al. [15] and matching the bound of Anand et al. [3] for the special case of fixed speed unrelated machines. Unlike the previous results most of which used an amortized local competitiveness argument or dual fitting methods,  use a primal-dual method, which is useful not only to analyze the algorithms but also to design the algorithm itself.
['Nikhil R. Devanur', 'Zhiyi Huang']
I am writing a research paper on a idea Primal dual gives almost optimal energy efficient online algorithms
[{"from": "human", "value": "I am writing a research paper on a idea Primal dual gives almost optimal energy efficient online algorithms"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of online scheduling of jobs on unrelated machines with dynamic speed scaling to minimize the sum of energy and ighted flow time.  give an algorithm with an almost optimal competitive ratio for arbitrary por functions. (No earlier results handled arbitrary por functions for minimizing flow time plus energy with unrelated machines.) For por functions of the form f(s) = s\u03b1 for some constant \u03b1 > 1,  get a competitive ratio of O(\u03b1/log \u03b1), improving upon a previous competitive ratio of O(\u03b12) by Anand et al. [3], along with a matching lor bound of \u03a9(\u03b1/log \u03b1). Further, in the resource augmentation model, with a 1 + e speed up,  give a 2(1/e + 1) competitive algorithm, with essentially the same techniques, improving the bound of 1 + O(1/e2) by Gupta et al. [15] and matching the bound of Anand et al. [3] for the special case of fixed speed unrelated machines. Unlike the previous results most of which used an amortized local competitiveness argument or dual fitting methods,  use a primal-dual method, which is useful not only to analyze the algorithms but also to design the algorithm itself."}]