Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the paper  consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s1 s2 s3 s4; respectively. Our aim is to find a schedule with a minimum possible length.  assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incompatibility graph of degree , where two incompatible jobs cannot be processed on the same machine.  show that the problem is NP-hard even if s1 = s2 = s3. If, hover, 4 and s1 12s2, s2 = s3 = s4, then the problem can be solved to optimality in time O(n 1:5 ). The same algorithm returns a solution of value at most 2 times optimal provided that s1 2s2. Finally,  study the case s1 s2 s3 = s4 and give an O(n 1:5 )-time 32=15-approximation algorithm in
['Hanna Furmańczyk', 'Marek Kubale']
I am writing a research paper on a idea Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines
[{"from": "human", "value": "I am writing a research paper on a idea Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the paper  consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s1 s2 s3 s4; respectively. Our aim is to find a schedule with a minimum possible length.  assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incompatibility graph of degree , where two incompatible jobs cannot be processed on the same machine.  show that the problem is NP-hard even if s1 = s2 = s3. If, hover, 4 and s1 12s2, s2 = s3 = s4, then the problem can be solved to optimality in time O(n 1:5 ). The same algorithm returns a solution of value at most 2 times optimal provided that s1 2s2. Finally,  study the case s1 s2 s3 = s4 and give an O(n 1:5 )-time 32=15-approximation algorithm in"}]