Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study reachability and deadlock detection questions in multi-stage scheduling systems. The jobs have partially ordered processing plans that dictate the order in which the job passes through the machines. Our results draw a sharp borderline beten tractable and intractable cases of these questions: certain types of processing plans (that  call unconstrained and source-constrained) lead to algorithmically tractable problems, whereas all remaining processing plans lead to NP-hard problems.#R##N##R##N# give conditions under which safe system states can be recognized in polynomial time, and  prove that without these conditions the recognition of safe system states is NP-hard.  show that deciding reachability of a given state is essentially equivalent to deciding safety. Finally,  establish NP-hardness of deciding whether the system can ever fall into a deadlock state.
['Cej Christian Eggermont', 'Gerhard J. Woeginger']
I am writing a research paper on a idea Reachability and deadlocking problems in multi-stage scheduling
[{"from": "human", "value": "I am writing a research paper on a idea Reachability and deadlocking problems in multi-stage scheduling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study reachability and deadlock detection questions in multi-stage scheduling systems. The jobs have partially ordered processing plans that dictate the order in which the job passes through the machines. Our results draw a sharp borderline beten tractable and intractable cases of these questions: certain types of processing plans (that  call unconstrained and source-constrained) lead to algorithmically tractable problems, whereas all remaining processing plans lead to NP-hard problems.#R##N##R##N# give conditions under which safe system states can be recognized in polynomial time, and  prove that without these conditions the recognition of safe system states is NP-hard.  show that deciding reachability of a given state is essentially equivalent to deciding safety. Finally,  establish NP-hardness of deciding whether the system can ever fall into a deadlock state."}]