I have lets say a \"travel date\" and black out dates. I will split the travel date into pieces according to the black out dates.
Note: Travel Date can be between          
        
This returns a discrete list of all dates that exist in the Travel Dates range but not in the Blackout Dates list, and then combines them using Oracle - Convert value from rows into ranges:
WITH traveldate AS
  (SELECT TO_DATE('2011 01 04','YYYY MM DD') AS start_date
         ,TO_DATE('2011 12 11','YYYY MM DD') AS end_date FROM DUAL)
    ,blackout AS
  (SELECT TO_DATE('2010 11 01','YYYY MM DD') AS start_date
         ,TO_DATE('2011 02 11','YYYY MM DD') AS end_date FROM DUAL
   UNION ALL
   SELECT TO_DATE('2011 01 20','YYYY MM DD') AS start_date
         ,TO_DATE('2011 02 15','YYYY MM DD') AS end_date FROM DUAL
   UNION ALL
   SELECT TO_DATE('2011 03 13','YYYY MM DD') AS start_date
         ,TO_DATE('2011 04 10','YYYY MM DD') AS end_date FROM DUAL
   UNION ALL
   SELECT TO_DATE('2011 03 20','YYYY MM DD') AS start_date
         ,TO_DATE('2011 06 29','YYYY MM DD') AS end_date FROM DUAL)
    ,days AS
  (SELECT TO_DATE('2010 01 01','YYYY MM DD') + ROWNUM d
   FROM DUAL CONNECT BY LEVEL <= 1000)
    ,base AS
  (SELECT d AS n
   FROM   days, traveldate
   WHERE  d >= traveldate.start_date AND d <= traveldate.end_date
   MINUS
   SELECT d AS n
   FROM   days, blackout
   WHERE  d >= blackout.start_date AND d <= blackout.end_date
  )
,lagged AS
(
    SELECT n, LAG(n) OVER (ORDER BY n) lag_n FROM base
)
, groups AS
(
    SELECT n, row_number() OVER (ORDER BY n) groupnum
      FROM lagged
      WHERE lag_n IS NULL OR lag_n < n-1
)
, grouped AS
(
    SELECT n, (SELECT MAX(groupnum) FROM groups
                 WHERE groups.n <= base.n
              ) groupnum
      FROM base
)
SELECT groupnum, MIN(n), MAX(n)
  FROM grouped
  GROUP BY groupnum
  ORDER BY groupnum;
Result:
GROUPNUM    MIN(N)          MAX(N)
1           16/02/2011  12/03/2011
2           30/06/2011  11/12/2011
Your tables:
SQL> create table travel (start_date,end_date)
  2  as
  3  select date '2011-01-04', date '2011-12-11' from dual
  4  /
Table created.
SQL> create table black_out_dates (bo,start_date,end_date)
  2  as
  3  select 'A', date '2010-11-01', date '2011-02-11' from dual union all
  4  select 'B', date '2011-01-20', date '2011-02-15' from dual union all
  5  select 'C', date '2011-03-13', date '2011-04-10' from dual union all
  6  select 'D', date '2011-03-20', date '2011-06-29' from dual
  7  /
Table created.
And the query, which takes into account completely overlapping black out periods:
SQL> select 'X' || to_char(row_number() over (order by new_start_date)) new_travel
  2       , new_start_date
  3       , new_end_date
  4    from ( select end_date + 1 new_start_date
  5                , lead(start_date - 1, 1, t_end_date) over (order by start_date) new_end_date
  6             from ( select start_date
  7                         , end_date
  8                         , t_end_date
  9                         , row_number() over (order by start_date) rn_start_date
 10                         , row_number() over (order by end_date) rn_end_date
 11                      from ( select bo.start_date
 12                                  , bo.end_date
 13                                  , t.end_date t_end_date
 14                               from black_out_dates bo
 15                                  , travel t
 16                              where t.start_date <= bo.end_date
 17                                and t.end_date >= bo.start_date
 18                              union all
 19                             select start_date - 1
 20                                  , start_date - 1
 21                                  , null
 22                               from travel
 23                           )
 24                  )
 25            where rn_start_date <= rn_end_date
 26         )
 27   where new_start_date <= new_end_date
 28   order by new_start_date
 29  /
NEW_TRAVEL NEW_START_DATE      NEW_END_DATE
---------- ------------------- -------------------
X1         16-02-2011 00:00:00 12-03-2011 00:00:00
X2         30-06-2011 00:00:00 11-12-2011 00:00:00
2 rows selected.
If your black_out_dates table contains N rows, then there at most N+1 gaps. The query makes up one dummy black out date period at [2011-01-03,2011-01-03], and then uses the analytic function LEAD to determine where the next black out date starts. Completely overlapping periods are removed by the ROW_NUMBER analytic functions, because they mess up the gap periods.
EDIT 14-3-2011
With these tables:
SQL> create table travel (start_date,end_date)
  2  as
  3  select date '2001-01-04', date '2013-12-11' from dual
  4  /
Table created.
SQL> create table black_out_dates (bo,start_date,end_date)
  2  as
  3  select 'A', date '2010-11-01', date '2011-02-11' from dual union all
  4  select 'B', date '2011-01-20', date '2011-02-15' from dual union all
  5  select 'C', date '2011-03-13', date '2011-04-10' from dual union all
  6  select 'D', date '2011-03-20', date '2011-06-29' from dual
  7  /
Table created.
My previous query still did not handle overlapping periods correctly. So here is a revised version, conveniently stored in view v:
SQL> create view v
  2  as
  3  with t1 as
  4  ( select bo.start_date
  5         , bo.end_date
  6         , t.end_date t_end_date
  7      from black_out_dates bo
  8         , travel t
  9     where bo.start_date <= t.end_date
 10       and bo.end_date >= t.start_date
 11     union all
 12    select start_date - 1
 13         , start_date - 1
 14         , end_date
 15      from travel
 16  )
 17  , t2 as
 18  ( select t1.*
 19         , nvl
 20           ( max(end_date)
 21             over
 22             ( order by start_date,end_date desc
 23               rows between unbounded preceding and 1 preceding
 24             )
 25           , to_date('1','j')
 26           ) max_date
 27      from t1
 28  )
 29  , t3 as
 30  ( select start_date
 31         , end_date
 32         , t_end_date
 33         , sum( case when start_date > max_date then 1 else 0 end )
 34           over
 35           ( order by start_date, end_date desc ) grp
 36      from t2
 37  )
 38  , t4 as
 39  ( select max(end_date) + 1 new_start_date
 40         , lead(min(start_date) - 1, 1, t_end_date) over (order by min(start_date)) new_end_date
 41      from t3
 42     group by t_end_date
 43         , grp
 44  )
 45  select new_start_date
 46       , new_end_date
 47    from t4
 48   where new_start_date <= new_end_date
 49  /
View created.
And the test results:
SQL> set feedback off
SQL> remark  Test 1
SQL> select * from v
  2  /
NEW_START_DATE      NEW_END_DATE
------------------- -------------------
04-01-2001 00:00:00 31-10-2010 00:00:00
16-02-2011 00:00:00 12-03-2011 00:00:00
30-06-2011 00:00:00 11-12-2013 00:00:00
SQL> remark  Test 2
SQL> delete travel
  2  /
SQL> delete black_out_dates
  2  /
SQL> INSERT INTO TRAVEL(  START_DATE, END_DATE )                 VALUES (   DATE '2011-01-01', DATE '2011-12-31' );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'A',  DATE '2011-02-02', DATE '2011-05-06' );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'B',  DATE '2011-03-03', DATE '2011-03-05'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'C',  DATE '2011-07-07', DATE '2011-07-09'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'D',  DATE '2011-07-08', DATE '2011-07-20'  );
SQL> select * from v
  2  /
NEW_START_DATE      NEW_END_DATE
------------------- -------------------
01-01-2011 00:00:00 01-02-2011 00:00:00
07-05-2011 00:00:00 06-07-2011 00:00:00
21-07-2011 00:00:00 31-12-2011 00:00:00
SQL> remark  Test 3
SQL> delete travel
  2  /
SQL> delete black_out_dates
  2  /
SQL> INSERT INTO TRAVEL(  START_DATE, END_DATE )                 VALUES (   DATE '2011-04-02', DATE '2011-10-20'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'A',  DATE '2011-01-01', DATE '2011-05-03'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'B',  DATE '2011-06-04', DATE '2011-06-20'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'C',  DATE '2011-06-06', DATE '2011-06-08'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'D',  DATE '2011-08-08', DATE '2011-12-30'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'E',  DATE '2011-08-08', DATE '2011-12-30'  );
SQL> select * from v
  2  /
NEW_START_DATE      NEW_END_DATE
------------------- -------------------
04-05-2011 00:00:00 03-06-2011 00:00:00
21-06-2011 00:00:00 07-08-2011 00:00:00
SQL> remark  Test 4
SQL> delete travel
  2  /
SQL> delete black_out_dates
  2  /
SQL> INSERT INTO TRAVEL(  START_DATE, END_DATE )                 VALUES (   DATE '2011-02-10', DATE '2011-05-15'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'A',  DATE '2011-02-02', DATE '2011-02-15'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'B',  DATE '2011-02-10', DATE '2011-02-20'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'C',  DATE '2011-04-10', DATE '2011-04-25'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'D',  DATE '2011-04-15', DATE '2011-04-20'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'E',  DATE '2011-05-10', DATE '2011-05-20'  );
SQL> select * from v
  2  /
NEW_START_DATE      NEW_END_DATE
------------------- -------------------
21-02-2011 00:00:00 09-04-2011 00:00:00
26-04-2011 00:00:00 09-05-2011 00:00:00
SQL> remark  Test 5
SQL> delete travel
  2  /
SQL> delete black_out_dates
  2  /
SQL> INSERT INTO TRAVEL VALUES (   DATE '2011-02-10', DATE '2011-05-17'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'A',  DATE '2011-02-05', DATE '2011-02-20'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'B',  DATE '2011-02-07', DATE '2011-02-09'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'C',  DATE '2011-05-05', DATE '2011-05-20'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'D',  DATE '2011-05-07', DATE '2011-05-15'  );
SQL> INSERT INTO BLACK_OUT_DATES( BO, START_DATE, END_DATE ) VALUES ( 'E',  DATE '2011-05-09', DATE '2011-05-12'  );
SQL> select * from v
  2  /
NEW_START_DATE      NEW_END_DATE
------------------- -------------------
21-02-2011 00:00:00 04-05-2011 00:00:00
SQL> remark  Test 6
SQL> delete travel
  2  /
SQL> delete black_out_dates
  2  /
SQL> INSERT INTO TRAVEL VALUES (DATE '2011-02-10', DATE '2011-09-20' );
SQL> INSERT INTO BLACK_OUT_DATES VALUES ('A', DATE '2011-01-05', DATE '2011-10-10' );
SQL> select * from v
  2  /
Regards,
Rob.