Embodiments of the present disclosure set forth methods for selecting a preferred data set. The methods include generating a joined relation based on a first relation having a first join attribute and a first existence probability attribute, and a second relation having a second join attribute compatible with the first join attribute and a second existence probability attribute, wherein the joined relation comprises a skyline probability attribute based at least in part on the product of a second value of the first existence probability attribute and a third value of the second existence probability attribute; and selecting, by one or more processors, the preferred data set from the joined relation based on a comparison of the first value of the skyline probability attribute and a predetermined threshold.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for selecting a preferred data set, comprising: generating, by one or more processors, a joined relation (joined relation) based on a first relation (first relation) having a first join attribute and a first existence probability attribute, and a second relation (second relation) having a second join attribute compatible with the first join attribute and a second existence probability attribute, wherein the joined relation comprises a skyline probability attribute based at least in part on the product of a second value of the first existence probability attribute and a third value of the second existence probability attribute; selecting, by one or more processors, the preferred data set (skyline) from the joined relation based on a comparison of the first value of the skyline probability attribute and a predetermined threshold. 2. The method of claim 1, before the generating, further comprising processing the first relation to retain a first set of tuples which are not fully dominated. (“first set of tuples” refers to Af) 3. The method of claim 2, before the generating, further comprising processing the second relation to retain a second set of tuples (“second set of tuples” refers to Bf) which are not fully dominated and selecting a first tuple (“first tuple” refers to Bfl) from the second set of tuples, wherein the first tuple locally dominates a second tuple from the second set of tuples. 4. The method of claim 3, wherein the joined relation comprises a first joined tuple joined based on the first tuple selected from the second set of tuples and a third tuple selected from the first set of tuples. (Theorem 1 of solution report) 5. The method of claim 4, wherein the first value of the skyline probability attribute of the first joined tuple is the product of the second value of the first existence probability attribute and the third value of the second existence probability attribute. (Theorem 1 of solution report) 6. The method of claim 1, before the generating, further comprising processing the first relation to retain a third set of tuples which are fully dominated. (“third set of tuples” refers to Af′) 7. The method of claim 3, wherein the joined relation comprises a second joined tuple joined based on the first tuple selected from the second set of tuples and a fourth tuple selected from the third set of tuples. (Theorem 2 of solution report) 8. The method of claim 7, wherein the selecting further comprises: comparing the second joined tuple with one or more target tuples in the joined relation to determine whether the second joined tuple is fully dominated by the one or more target tuples, wherein the one or more target tuples comprise tuples formed by joining the first tuple with tuples in the first relation; and selecting the second joined tuple if it is determined that the second joined tuple is not dominated by the one or more target tuples. 9. The method of claim 8, wherein a fourth value of the skyline probability attribute of the second joined tuple is the product of the existence probability of the first tuple selected from the second set of tuples and the existence probability of the fourth tuple selected from the third set of tuples. 10. The method of claim 3, further comprising identifying a fifth tuple (“fifth tuple” refers to Bfl′1) of the second relation which locally dominates the second tuple (“second tuple” refers to Bfl′1). (Iterative approach) 11. The method of claim 3, further comprising identifying a dominance relationship among the first tuple and other tuples in the second relation based on a first local attribute of the second relation. (dominator-based approach) 12. The method of claim 1, wherein the first existence probability attribute is generated from a product of a first probability and a second probability of a first locationally uncertain tuple in the first relation. 13. A computer-readable storage medium encoded with computer-executable instructions for selecting a preferred data set, which when executed by a computing device, causes the computing device to: generate, by one or more processors, a joined relation based on a first relation having a first join attribute and a first existence probability attribute, and a second relation having a second join attribute compatible with the first join attribute and a second existence probability attribute, wherein the joined relation comprises a skyline probability attribute based at least in part on the product of a second value of the first existence probability attribute and a third value of the second existence probability attribute; and select, by one or more processors, the preferred data set from the joined relation based on a comparison of the first value of the skyline probability attribute and a predetermined threshold. 14. The computer-readable storage medium of claim 13, further encoded with computer-executable instructions for, before the generating a joined relation, processing the first relation to retain a first set of tuples which are not fully dominated. 15. The computer-readable storage medium of claim 14, further encoded with computer-executable instructions for, before the generating a joined relation, processing the second relation to retain a second set of tuples which are not fully dominated and selecting a first tuple from the second set of tuples, wherein the first tuple locally dominates a second tuple from the second set of tuples. 16. The computer-readable storage medium of claim 15, wherein the joined relation comprises a first joined tuple joined based on the first tuple selected from the second set of tuples and a third tuple selected from the first set of tuples. 17. The computer-readable storage medium of claim 16, wherein the first value of the skyline probability attribute of the first joined tuple is the product of the second value of the first existence probability attribute and the third value of the second existence probability attribute. 18. The computer-readable storage medium of claim 13, further encoded with computer-executable instructions for, before the generating a joined relation, processing the first relation to retain a third set of tuples which are fully dominated. 19. The computer-readable storage medium of claim 15, wherein the joined relation comprises a second joined tuple joined based on the first tuple selected from the second set of tuples and a fourth tuple selected from the third set of tuples. 20. The computer-readable storage medium of claim 19, further encoded with computer-executable instructions for, comparing the second joined tuple with one or more target tuples in the joined relation to determine whether the second joined tuple is fully dominated by the one or more target tuples, wherein the one or more target tuples comprise tuples formed by joining the first tuple with tuples in the first relation; and selecting the second joined tuple if it is determined that the second joined tuple is not dominated by the one or more target tuples. 21. The computer-readable storage medium of claim 20, wherein a fourth value of the skyline probability attribute of the second joined tuple is the product of the existence probability of the first tuple selected from the second set of tuples and the existence probability of the fourth tuple selected from the third set of tuples. 22. The computer-readable storage medium of claim 15, further encoded with computer-executable instructions for identifying a fifth tuple of the second relation which locally dominates the second tuple. 23. The computer-readable storage medium of claim 15, further encoded with computer-executable instructions for identifying a dominance relationship among the first tuple and other tuples in the second relation based on a first local attribute of the second relation. 24. The computer-readable storage medium of claim 13, wherein the first existence probability attribute is generated from a product of a first probability and a second probability of a first locationally uncertain tuple in the first relation. 25. A computing device configured to select a preferred data set, comprising: a processing unit, wherein the processing unit is configured to generate, by one or more processors, a joined relation based on a first relation having a first join attribute and a first existence probability attribute, and a second relation having a second join attribute compatible with the first join attribute and a second existence probability attribute, wherein the joined relation comprises a skyline probability attribute based at least in part on the product of a second value of the first existence probability attribute and a third value of the second existence probability attribute; and select, by one or more processors, the preferred data set from the joined relation based on a comparison of the first value of the skyline probability attribute and a predetermined threshold. 26. The computing device of claim 13, wherein the processing unit is further configured to, before the generating a joined relation, process the first relation to retain a first set of tuples which are not fully dominated. 27. The computing device of claim 26, wherein the processing unit is further configured to, before the generating a joined relation, process the second relation to retain a second set of tuples which are not fully dominated and selecting a first tuple from the second set of tuples, wherein the first tuple locally dominates a second tuple from the second set of tuples. 28. The computing device of claim 27, wherein the joined relation comprises a first joined tuple joined based on the first tuple selected from the second set of tuples and a third tuple selected from the first set of tuples. 29. The computing device of claim 28, wherein the first value of the skyline probability attribute of the first joined tuple is the product of the second value of the first existence probability attribute and the third value of the second existence probability attribute. 30. The computing device of claim 25, wherein the processing unit is further configured to, before the generating a joined relation, process the first relation to retain a third set of tuples which are fully dominated. 31. The computing device of claim 27, wherein the joined relation comprises a second joined tuple joined based on the first tuple selected from the second set of tuples and a fourth tuple selected from the third set of tuples. 32. The computing device of claim 31, wherein the processing unit is further configured to: compare the second joined tuple with one or more target tuples in the joined relation to determine whether the second joined tuple is fully dominated by the one or more target tuples, wherein the one or more target tuples comprise tuples formed by joining the first tuple with tuples in the first relation; and select the second joined tuple if it is determined that the second joined tuple is not dominated by the one or more target tuples. 33. The computing device of claim 32, wherein a fourth value of the skyline probability attribute of the second joined tuple is the product of the existence probability of the first tuple selected from the second set of tuples and the existence probability of the fourth tuple selected from the third set of tuples. 34. The computing device of claim 27, wherein the processing unit is further configured to identify a fifth tuple of the second relation which locally dominates the second tuple. 35. The computing device of claim 27, wherein the processing unit is further configured to identify a dominance relationship among the first tuple and other tuples in the second relation based on a first local attribute of the second relation. 36. The computing device of claim 25, wherein the first existence probability attribute is generated from a product of a first probability and a second probability of a first locationally uncertain tuple in the first relation.