Projector connectivity proved to be NP-hard
Computer scientists from the European Center of Fundamental Research have published a peer-reviewed paper titled "Applications of The Szemerédi's Regularity Lemma to Acyclic Graph Connectivity of Video Projection Hardware". The important conclusion of the research is the proof of impossibility of establishing a stable connection on the first try when connecting a projector to a laptop.
It doesn't matter whether VGA, HDMI or DP port is used. The software also does not play a role in rectifying the issue.
"[It] seems to be another fundamental limitation of the Universe, a property similar to speed of light or causation itself. We all knew this deep in our hearts, but couldn't prove before." comments Gustavo Sanchez, one of the authors of the paper.
A successful, stable connection on the first try is theoretically possible if and only if P=NP, which remains to be one of the core unsolved problems in computer science.
Projector manufacturers are expected to decrease budgets related to customer support and satisfaction guarantees.