Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the average completion time (k-Traveling Repairman Problem).  give competitive algorithms, resource augmentation results and lor bounds for k-server routing problems on several classes of metric spaces. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely,  give a 1+O((logk)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line.  also prove that similar results cannot hold for the Euclidean plane.
['Vincenzo Bonifaci', 'Leen Stougie']
I am writing a research paper on a idea Online k -server routing problems
[{"from": "human", "value": "I am writing a research paper on a idea Online k -server routing problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the average completion time (k-Traveling Repairman Problem).  give competitive algorithms, resource augmentation results and lor bounds for k-server routing problems on several classes of metric spaces. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely,  give a 1+O((logk)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line.  also prove that similar results cannot hold for the Euclidean plane."}]