Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a generalization of the coupled-task scheduling problem introduced by Shapiro (Shapiro 1980), where considered tasks are subject to incompatibility constraint depicted by an undirected graph. The motivation of this problem comes from data acquisition and processing in a mono-processor torpedo used for underwater exploration. As  add the compatibility graph,  focus on complexity of the problem, and more precisely on the border beten P and NP-completeness when some other input parameters are restricted (e.g. the ratio beten the durations of the two sub-tasks composing a task):  adapt the global visualization of the complexity of scheduling problems with coupled-task given by Orman and Potts (Orman and Potts 1997) to our problem, determine new complexity results, and thus propose a new visualization including incompatibility constraint. In the end,  give a new polynomial-time approximation algorithm result which completes previous works.
['Gilles Simonin', 'Rodolphe Giroudeau', 'Jean-Claude König', 'Benoit Darties']
I am writing a research paper on a idea Theoretical aspects of scheduling coupled-tasks in the presence of compatibility graph
[{"from": "human", "value": "I am writing a research paper on a idea Theoretical aspects of scheduling coupled-tasks in the presence of compatibility graph"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a generalization of the coupled-task scheduling problem introduced by Shapiro (Shapiro 1980), where considered tasks are subject to incompatibility constraint depicted by an undirected graph. The motivation of this problem comes from data acquisition and processing in a mono-processor torpedo used for underwater exploration. As  add the compatibility graph,  focus on complexity of the problem, and more precisely on the border beten P and NP-completeness when some other input parameters are restricted (e.g. the ratio beten the durations of the two sub-tasks composing a task):  adapt the global visualization of the complexity of scheduling problems with coupled-task given by Orman and Potts (Orman and Potts 1997) to our problem, determine new complexity results, and thus propose a new visualization including incompatibility constraint. In the end,  give a new polynomial-time approximation algorithm result which completes previous works."}]