Sequential metric dimension for random graphs

In the localization game on a graph, goal is to find fixed but unknown target node $v^\star$ with least number of distance queries possible. $j^{th}$ step game, player single $v_j$ and receives, as an answer their query, between nodes $v^\star$. The sequential metric dimension (SMD) minimal that needs guess absolute certainty, no matter where is. term SMD originates from related notion (MD), which can be defined same way SMD, except player's are non-adaptive. this work, we extend results \cite{bollobas2012metric} MD Erd\H{o}s-R\'enyi graphs SMD. We that, in connected graphs, constant factor apart. For lower bound present clean analysis by combining tools developed for novel coupling argument. upper show strategy greedily minimizes candidate targets each uses asymptotically optimal graphs. Connections source localization, binary search birthday problem discussed.