| Input: : number of inner objects retrieved for an outer object, : outer segment, : set of inner objects |
| Output: : set of ordered pairs of outer object and inner object |
| (1) | if then // denotes that contains only an outer object , that is, |
| (2) | // kNN query from is performed and its result is saved to |
| (3) | // a partial join result for is generated from |
| (4) | return // a partial join result for is returned |
| (5) | else if then // denotes that contains only two outer objects and |
| (6) | // kNN query from is performed, and its result is saved to |
| (7) | // a partial join result for is generated from |
| (8) | // kNN query from is performed, and its result is saved to |
| (9) | // a partial join result for is generated from |
| (10) | return // the union of the partial join results for and is returned |
| (11) | else if then // denotes that contains more than three outer objects |
| (12) | // kNN query from is performed, and its result is saved to |
| (13) | // a partial join result for is generated from |
| (14) | // kNN query from is performed, and its result is saved to |
| (15) | // a partial join result for is generated from |
| (16) | // inner objects located in are retrieved |
| (17) | for each outer object do // k NNs of outer objects are retrieved from |
| (18) | // is explained in Algorithm 4 |
| (19) | // a partial join result for is generated from |
| (20) | return // the union of the partial join results for is returned |
