declare @result table (ID1 int, ID2 int)

declare @t table (ID1 int, ID2 int)
insert into @t values
(1, 1),
(2, 1),
(3, 1),
(1, 3),
(2, 3),
(3, 3),
(1, 4),
(2, 4),
(3, 4)

-- select * from @t

while 1 = 1 
begin
	insert into @result(ID1, ID2)	
	select top 1
		ID1, min(ID2) 
	from @t t
	where not exists(select 1 from @result r where t.ID1=r.ID1 or t.ID2=r.ID2)
	group by ID1
	order by ID1;
	--
	if @@ROWCOUNT = 0 break;
end

select * from @result

declare @result table (ID1 int, ID2 int)

declare @t table (ID1 int, ID2 int)
insert into @t values
(1, 1),
(2, 1),
(3, 1),
(1, 3),
(2, 5),
(3, 3),
(1, 4),
(2, 4),
(3, 4)

select id1, id2 from
   (select id1, row_number() over(order by id1) rn
      from (select distinct id1 from @t) t) d1
   full outer join
   (select id2, row_number() over(order by id2) rn
      from (select distinct id2 from @t) t) d2
   on d1.rn = d2.rn