The Banker's problem with precedences

AbstractSeveral interesting generalizations of the Banker's problem, as a deadlock avoidance problem, are examined. We first allow each task to return after its execution, more resource units than it requires or vice versa. We allow precedences between the tasks which partially define the order of execution, and finally we allow resources of more than one kind. We prove that the problem becomes NP-complete in the two latter cases and we present two interesting subcases (among them the subcase where the precedences have a “forest” structure), where it can be solved in polynomial time