  In 5G, the Physical Downlink Control CHannel (PDCCH) carries crucial
information enabling the User Equipment (UE) to connect in UL and DL. UEs are
unaware of the frequency location at which PDCCH is encoded, hence they need to
perform blind decoding over a limited set of possible candidates. We address
the problem faced by the gNodeB of selecting PDCCH candidates for each UE to
optimize data transmission. We formulate it as a Maximum Weighted Independent
Set (MWIS) problem, that is known to be an NP-hard problem and cannot even be
approximated. A solution method called Weight-to-Degree Ratio (WDR) Greedy
emerges as a strong contender for practical implementations due to its
favorable performance-to-complexity trade-off and theoretical performance
guarantees.
