use tempdb;
set ansi_nulls, quoted_identifier, xact_abort on;
go

create table dbo.t (id int identity primary key, g int, v float);

insert into dbo.t
 (g, v)
 select top (2000000)
  row_number() over (order by 1/0) % 10,
  rand(checksum(newid()))
 from
  master.dbo.spt_values a cross join
  master.dbo.spt_values b;

create index IX_t__g__v on dbo.t (g, v);
go

declare @g int, @v float;

set statistics time on;
--set statistics xml on;

with t as
(
 select
  g, v, row_number() over (partition by g order by v) as rn
 from
  dbo.t
)
select
 @g = g, @v = v
from
 t
where
 rn = 1
option
 (maxdop 1);

select top (1) with ties
 @g = g, @v = v 
from
 dbo.t
order by
 row_number() over (partition by g order by v)
option
 (maxdop 1);

set statistics time off;
--set statistics xml off;
 
drop table dbo.t;
go

 SQL Server Execution Times:
   CPU time = 125 ms,  elapsed time = 132 ms.

 SQL Server Execution Times:
   CPU time = 437 ms,  elapsed time = 441 ms.