Postgresql – If i index two columns (indepentently) do i get the same performance as putting and index on the two

Answer

Since you refer to the website use-the-index-luke.com, consider the chapter:

Use The Index, Luke › The Where Clause › Searching For Ranges › Greater, Less and BETWEEN

It has an example that matches your situation perfectly (two-column index, one is tested for equality, the other for range), explains (with more of those nice index graphics) why @ypercube's advice is accurate and sums it up:

Rule of thumb: index for equality first — then for ranges.

Also good for just one column?

What to do for queries on just one column seems to be clear. More details and benchmarks concerning that under these related question:

• Working of indexes in PostgreSQL
• Is a composite index also good for queries on the first field?

Less selective column first?

Apart from that, what if you have only equality conditions for both columns?

It doesn't matter. Put the column first that is more likely to receive conditions of its own, which actually matters.

Consider this demo, or reproduce it yourself. I create a simple table of two columns with 100k rows. One with very few, the other one with lots of distinct values:

CREATE TEMP TABLE t AS
SELECT (random() * 10000)::int AS lots
     , (random() * 4)::int     AS few
FROM generate_series (1, 100000);

DELETE FROM t WHERE random() > 0.9;  -- create some dead tuples, more "real-life"

ANALYZE t;

SELECT count(distinct lots)   -- 9999
     , count(distinct few)    --    5
FROM   t;

Query:

SELECT *
FROM   t
WHERE  lots = 2345
AND    few = 2;

EXPLAIN ANALYZE output (Best of 10 to exclude caching effects):

Seq Scan on t  (cost=0.00..5840.84 rows=2 width=8)
               (actual time=5.646..15.535 rows=2 loops=1)
  Filter: ((lots = 2345) AND (few = 2))
  Buffers: local hit=443
Total runtime: 15.557 ms

Add index, retest:

CREATE INDEX t_lf_idx ON t(lots, few);

Index Scan using t_lf_idx on t  (cost=0.00..3.76 rows=2 width=8)
                                (actual time=0.008..0.011 rows=2 loops=1)
  Index Cond: ((lots = 2345) AND (few = 2))
  Buffers: local hit=4
Total runtime: 0.027 ms

Add other index, retest:

DROP INDEX t_lf_idx;
CREATE INDEX t_fl_idx  ON t(few, lots);

Index Scan using t_fl_idx on t  (cost=0.00..3.74 rows=2 width=8)
                                (actual time=0.007..0.011 rows=2 loops=1)
  Index Cond: ((few = 2) AND (lots = 2345))
  Buffers: local hit=4
Total runtime: 0.027 ms

Can i replace the non-clustered indices with one covering index ?

No. Suppose you sometimes find people by LastName and sometimes by FirstName. An index on (LastName, FirstName) won't help you find people by FirstName.

If not, is there any way to get rid of RID Lookup rather than a covering index ?

Not in a way that's particularly useful.

Does each query require a different covering index depending on the columns in the select list and the search conditions ?

Pretty much. Your job is to come up with a compromise.

I have no clustered indexes in the table , does adding a unique column and setting it as a primary key helps in getting rid of RID Lookups ?

A PK doesn't necessarily mean a clustered index. And having a CIX just means your RID Lookups will become Key Lookups, which are potentially worse. But without CIXs you have heaps which can fragment when you change or delete data. So CIXs are fine, but won't improve performance of your Lookups.