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.

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