I have a table people(gid int, name varchar) with data:

gid    name                 
1      Bill
2      Will
2      Musk
2      Jack
1      Martin
1      Jorge

now I want to get a result set like below:

  gid   representative(varchar)
   1     Bill, Martin
   2     Will, Musk

I mean to list out each group with two of people’s names of that group as representative. Here the order doesn’t matter, the count matters. How to do it in one query statement, i.e. in PG?

After multiple trying for a long while, I can achieve the goal by this statement:

with indexed as(
    select id,name,row_number() over (partition by id) as index
    from people
),filtered as(
    select id, name 
    from indexed where index<3
)
select id,string_agg(name,',')
from filtered
group by id;

However, the actual table has huge number rows and more complicated schema. It consumes long time to just create the first CTE table “indexed” because of traversing the whole table.
Is there better resolution to direct database engine to select out just parts of rows for each group at first, without full traversing?