Should child nodes have a reference to their parents?

Let’s say you are engineering a chat room software.

let client = new Client();
let room = rooms.FindRoom();
room.addClient(client);

This room (parent) now has a client (child).

client.on('message', (event) => {
   // With the above code, room must be found
   let room = rooms.FindClientsRoom(client);
   if(room){
       room.handleMessage(event);
   }
});

Or we have a child that knows about its parent

let client = new Client();
let room = rooms.FindRoom();
room.addClient(client);
client.setRoom(room);


client.on('message', (event) => {
   let room = client.getRoom();
   if(room){
       room.handleMessage(event);
   }
});

This is incredibly fast compared to looking for a client within 1000s of rooms. But is there something wrong with the design pattern? In any system, such as XML, do child nodes know about their parents? Should they?