Skyline Query Challenge

Question

Suppose you are shopping for a new car, and are specifically looking for a big
car with decent gas mileage. Unfortunately, we are trying to satisfy the two
conflicting goals. If we are querying the Cars relation in the database, then we
certainly can ignore all models that are worse than others by both criteria. The
remaining set of cars is called the Skyline.
More formally the Skyline is defined as those points which are not dominated by
any other point. A point dominates the other point if it is as good or better in
all the dimensions. For example Roadster with mileage=20 and seating=2 dominates
Ferrari F1 with mileage=10 and seating=1. This condition can certainly be
expressed in SQL. In our example, the Skyline query is
select * from Cars c
where not exists (
select * from Cars cc
where cc.seats >= c.seats and cc.mileage > c.mileage
or cc.seats > c.seats and cc.mileage >= c.mileage
Despite apparent simplicity of this query, you I'm not pleased with this query
performance. Even if we index the seats and mileage columns, this wouldn’t help
much as only half of the records on average meet each individual inequality
condition. Certainly, there aren’t many records that satisfy the combined
predicate, but we can’t leverage index to match it. Bitmapped indexes, which
excel with Boolean expressions similar to what we have, demand a constant on one
side of the inequality predicate.
There is an efficient way to answer Skyline query. Order all the data by either
seats, mileage, or mileage, seats. Here a composite index might be handy.
Compare each record with its predecessor, and discard the one that is dominated
by the other. Let’s assume that our example has been extended to 4 records:
MANUFACTURER SEATS MILEAGE
Hummer 4 5
Ferrari 1 10
BMW 2 15
Roadster 2 20
Iterating record by record down, Ferrari would be excluded first, because it’s
dominated by the neighbor BMW. Then, BMW itself would be excluded, because it’s
dominated by Roadster.
The challenge is to express this algorithm (efficiently) in SQL. With or without Analytics.

Answer 1

Mike:
Performance aside, see if you can reproduce:
Connected to:
Oracle9i Enterprise Edition Release 9.2.0.6.0 - Production
With the Partitioning, Oracle Label Security, OLAP and Oracle Data Mining options
JServer Release 9.2.0.6.0 - Production
flip@FLOP> CREATE TABLE CARS
  2  (
  3  MANUFACTURER VARCHAR2(10 BYTE),
  4  SEATS NUMBER(2),
  5  MILEAGE NUMBER
  6  );
Table created.
Elapsed: 00:00:00.00
flip@FLOP>
flip@FLOP> insert into cars
  2  select to_char(object_id) , mod(object_id,7)+1, mod(object_id,25)+25
  3  from   all_objects where rownum < 101;
100 rows created.
Elapsed: 00:00:00.00
flip@FLOP>
flip@FLOP> insert into cars
  2  select 'x'||manufacturer, seats, mileage
  3  from    cars;
100 rows created.
Elapsed: 00:00:00.00
flip@FLOP>
flip@FLOP> commit;
Commit complete.
Elapsed: 00:00:00.00
flip@FLOP>
flip@FLOP> CREATE OR REPLACE FORCE VIEW CARS_VIEW
  2  (MANUFACTURER,SEATS, MILEAGE, LVL, RNM, SKLN_FLG)
  3  AS
  4  select
  5  MANUFACTURER,
  6  seats,
  7  mileage,
  8  level lvl,
  9  rownum rnm,
10  (
11  case when level=rownum then 1
12  else 0
13  end
14  ) skln_flg
15  from
16  (
17  select
18  MANUFACTURER,
19  seats,
20  mileage
21  from cars
22  order by mileage desc
23  )
24  connect by prior seats < seats ;
View created.
Elapsed: 00:00:00.00
flip@FLOP>
flip@FLOP> select
  2  c.* from cars c,
  3  (
  4  select mileage,seats from cars_view where rownum <
  5  (
  6  select rnm from cars_view
  7  where skln_flg=0
  8  and rownum < 2
  9  )
10  )sbq
11  where c.mileage = sbq.mileage
12  and c.seats = sbq.seats
13  ;
MANUFACTUR      SEATS    MILEAGE
9849                1         49
x9849               1         49
9249                3         49
x9249               3         49
x22724              3         49
22724               3         49
14424               5         49
x14424              5         49
15174               6         49
x15174              6         49
7349                7         49
x7349               7         49
12 rows selected.
Elapsed: 00:00:00.00
flip@FLOP>
flip@FLOP> select * from Cars c
  2  where not exists (
  3  select * from Cars cc
  4  where cc.seats >= c.seats and cc.mileage > c.mileage
  5  or cc.seats > c.seats and cc.mileage >= c.mileage
  6  );
MANUFACTUR      SEATS    MILEAGE
7349                7         49
x7349               7         49
Elapsed: 00:00:00.00
flip@FLOP>