Here your have the different algorihtm use into Catchchallenger for the visibility of player. Ordered by lower cpu usage to greater cpu usage.
Map visibility algorithm none
The other player position is not send. No cpu cost for that's, no network usage. Used in single player, in case of heavy load, very weak network and in case of DDOS (see Server under DDOS). Is fixed algorithmic complexity and near to be null.
Map visibility algorithm simple
Only the player on the same map is send. Then the player near but out of the border is not show. Correct of very low end cpu, or when the bottom algorithm do too hight load. That's do average network usage. The algorithmic complexity can be dropped to linear complexity and not square as the first implementation as see in lot of server.
Map visibility algorithm with border
Show all player on current map and border map. That's do hight quality show. But do hight network usage.
Map visibility algorithm with border and range
Show all player in range, include if is on the map border. Work with border to don't parse each player connected range. Do very minimal network usage, but at cost of hight cpu usage.