# How can I develop a pseudo-polynomial time algorithm for a non-integer problem?

I have an scheduling probelm with a set of jobs $$J$$, with a ''non-integer'' parameter $$\beta_j$$, i.e. the parameter is a real number and $$\beta_j \leqslant 0.5, \exists j \in J$$.

Since the problem will be trivial if $$\beta_j > 0.5, \forall j \in J$$, I can not assume that we may transform an instance to an integer one. By the way, I am looking for the computational complexity of the problem.

So my question is: How can I develop a pseudo-polynomial time algorithm for the problem (to indicate that it is at most NP-hard in the ordinary sense), although the problem is not integer-value?

• Thanks for the information. So you mean I should consider rational numbers for $\beta$. Then are you aware of some source that I can read to get familiar with analyzing complexity of ''normal computational problems''? – Mostafa Apr 12 '19 at 10:13