| Input: : number of inner objects retrieved for an outer object, : set of outer objects, : set of inner objects |
| Output: : set of ordered pairs of outer object and inner object |
| (1) | // kNN join result set is initialized to the empty set |
| (2) | // step 1: outer objects in a vertex sequence are grouped into an outer segment |
| (3) | // is explained in Algorithm 1 |
| (4) | // step 2: kNN join is evaluated for each outer segment |
| (5) | for each outer segment do |
| (6) | if then // see Figures 8(a) to 8(d) |
| (7) | // kNN query from is performed, and its result is saved to |
| (8) | // a partial join result for is generated from |
| (9) | |
| (10) | else if then // it is assumed that belongs to and that () is close to |
| (11) | if and then // see Figure 9(a) |
| (12) | // result of kNN query at is reused for other outer segment(s) |
| (13) | // result of kNN query at is reused for other outer segment(s) |
| (14) | // refer to Algorithm 6 |
| (15) | |
| (16) | else if and then // see Figure 9(b) |
| (17) | // result of kNN query at is reused for other outer segment(s) |
| (18) | // result of kNN query at is not reused |
| (19) | // refer to Algorithm 6 |
| (20) | |
| (21) | else if and then // see Figure 9(c) |
| (22) | // result of kNN query at is not reused |
| (23) | // result of kNN query at is reused for other outer segment(s) |
| (24) | // refer to Algorithm 6 |
| (25) | |
| (26) | else if and then // see Figure 9(d) |
| (27) | // result of kNN query at is not reused |
| (28) | // result of kNN query at is not reused |
| (29) | // refer to Algorithm 6 |
| (30) | |
| (31) | return // is returned after all outer segments have been processed |
