Consider the following snapshot of a system running $n$ processes. Process $i$ is holding $X_i$ instances of a resource $R$, $ 1\leq i\leq n$. Currently, all instances of $R$ are occupied. Further, for all $i$, process $i$ has placed a request for an additional $Y_i$ instances while holding the $X_i$ instances it already has. There are exactly two processes $p$ and $q$ and such that $Y_p=Y_q=0$. Which one of the following can serve as a necessary condition to guarantee that the system is not approaching a deadlock?
- $ \min(X_{p},X_{q})<\max(Y_i)\:\text{where}\:i!=p\:\text{and}\:i!=q$
- $ X_{p}+X_{q}\geq \min(Y_i)\:\text{where}\:i!=p\:\text{and}\:i!=q$
- $ \max(X_{p},X_{q})>1$
- $ \min(X_{p},X_{q})>1$
