In this letter, we assess the scalability of a path computation flooding (PCF) approach to compute optimal end-to-end inter-domain paths in a path computation element-based multi-domain network. PCF yields a drastically reduced network blocking probability compared to a blind per-domain path computation but introduces significant network control overhead and path computation complexity. In view of this, we introduce and compare an alternative low overhead PCF (LoPCF) solution. From the obtained results, LoPCF leads to similar blocking probabilities to PCF while exhibiting around 50% path computation complexity and network control overhead reduction.