Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a general class of scheduling problems where a set of  conflicting  jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the ighted sum of completion times. The conflicts among jobs are formed as an  arbitrary  conflict graph.   Building on the framework of Queyranne and Sviridenko [2002b],  present a general technique for reducing the ighted sum of completion-times problem to the classical makespan minimization problem. Using this technique,  improve the best-known results for scheduling conflicting jobs with the min-sum objective, on several fundamental classes of graphs, including line graphs, ( k  p 1)-claw-free graphs, and perfect graphs. In particular,  obtain the first constant-factor approximation ratio for nonpreemptive scheduling on interval graphs.  also improve the results of Kim [2003] for scheduling jobs on line graphs and for resource-constrained scheduling.
['Rajiv Gandhi', 'Magnús M. Halldórsson', 'Guy Kortsarz', 'Hadas Shachnai']
I am writing a research paper on a idea Improved bounds for scheduling conflicting jobs with minsum criteria
[{"from": "human", "value": "I am writing a research paper on a idea Improved bounds for scheduling conflicting jobs with minsum criteria"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a general class of scheduling problems where a set of  conflicting  jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the ighted sum of completion times. The conflicts among jobs are formed as an  arbitrary  conflict graph.   Building on the framework of Queyranne and Sviridenko [2002b],  present a general technique for reducing the ighted sum of completion-times problem to the classical makespan minimization problem. Using this technique,  improve the best-known results for scheduling conflicting jobs with the min-sum objective, on several fundamental classes of graphs, including line graphs, ( k  p 1)-claw-free graphs, and perfect graphs. In particular,  obtain the first constant-factor approximation ratio for nonpreemptive scheduling on interval graphs.  also improve the results of Kim [2003] for scheduling jobs on line graphs and for resource-constrained scheduling."}]