CMPS 340  File Processing
B^+-trees:  algorithms for insertion/deletion



Insert+(R):
  BEGIN
    find bucket M where R "belongs";  --depends entirely upon R.KEY
    place R into proper place within M;
    IF M is overflowing THEN
       IF M has an immediate sibling M' not on the verge of overflowing THEN
          redistribute from M to M'
          appropriately modify the separator of M and M' in their parent
       ELSE --redistribution not possible
          split M (i.e., allocate new bucket M' and move second half of
                         records in M into M')
          using the B-tree insertion algorithm, insert into their parent a
                   value that serves as a separator for M and M' 
       ENDIF
    ELSE --M not overflowing
       do nothing
    ENDIF
  END Insert;


Delete+(k):
  BEGIN
    find bucket M containing R, where R.KEY = k;
    remove R from M;
    IF M is underflowing THEN
       IF M has an immediate sibling M' not on verge of underflowing THEN
          redistribute from M' to M
          appropriately modify the separator of M and M' in their parent
       ELSE --redistribution not possible
          merge M and an immediate sibling M' (i.e., move all records of M
                into M' and then free the space used by M)
          using B-tree deletion algorithm, delete the separator of M and M'
                from their parent
       ENDIF
    ELSE --M not underflowing
       do nothing
    ENDIF
  END Delete;