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Online Interval Skyline Queries on Time Series

Online Interval Skyline Queries on Time Series. ICDE 2009. Outline. Introduction Interval Skyline Query Algorithm On-The-Fly (OTF) View-Materialization(VM) Experiment Conclusion. Introduction.

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Online Interval Skyline Queries on Time Series

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  1. Online Interval Skyline Queries on Time Series ICDE 2009

  2. Outline • Introduction • Interval Skyline Query • Algorithm • On-The-Fly (OTF) • View-Materialization(VM) • Experiment • Conclusion

  3. Introduction • A power supplier need to analyze the consumption of different regions in the service area.

  4. Interval Skyline Query • A time series s consists of a set of (timestamp, value) pairs. (Ex: A={(1,4) (2,3)} ) • Dominance Relation • Time series s is said to dominate time series q in interval [i : j], denoted by , if ∀k ∈ [i : j], s[k] ≥ q[k]; and ∃l ∈ [i : j], s[l] > q[l]. • Ex: Consider interval [1,2]

  5. Interval Skyline Query • Let be the most recent timestamp. We call interval the base interval. • Whenever a new timestamp +1 comes, the oldest one −w+1 expires. • Consequently, the base interval becomes • Problem Definition: Given a set of time series S such that each time series is in the base interval , we want to maintain a data structure D such that any interval skyline queries in interval [i:j] W can be answered efficiently using D.

  6. On-The-Fly (OTF) • The on the fly method keeps the minimum and maximum values for each time series. • Lemma: For two time series p,q and interval if then s dominates q in .

  7. On-The-Fly (OTF) Iteravively process the time series in S in their max value descending order Ex: Consider Let usCompute the skyline in interval [2,3]

  8. On-The-Fly (OTF)Candidate list {s2}

  9. On-The-Fly (OTF)Candidate list {s2,s3}

  10. On-The-Fly (OTF)Candidate list {s2,s3,s5}

  11. On-The-Fly (OTF)Candidate list {s2,s3,s5}

  12. On-The-Fly (OTF)Terminate and return candidate list

  13. Online Interval Skyline Query Answering • Radix priority search tree (5,8) (7,7) (4,6) (8,5) (1,4) (6,3) (3,2) (2,1)

  14. Online Interval Skyline Query Answering • Radix priority search tree (5,8) (7,7) (4,6) (8,5) (1,4) (6,3) (3,2) (2,1)

  15. Online Interval Skyline Query Answering • Radix priority search tree (5,8) (7,7) (4,6) (8,5) (1,4) (6,3) (3,2) (2,1)

  16. Online Interval Skyline Query Answering • Radix priority search tree (5,8) (7,7) (4,6) (8,5) (1,4) (6,3) (3,2) (2,1)

  17. Online Interval Skyline Query Answering • Radix priority search tree (5,8) (7,7) (4,6) (8,5) (1,4) (6,3) (3,2) (2,1)

  18. Online Interval Skyline Query Answering • Radix priority search tree (5,8) (7,7) (4,6) (8,5) (1,4) (6,3) (3,2) (2,1)

  19. Online Interval Skyline Query Answering • Maintaining a Radix Priority Search Tree for Each Time Series • To process a time series, we use the time dimension (i.e the timestamps) as the binary tree dimension X and data values as the heap dimension Y. • Since the base interval W always consists of w timestamps represent w consecutive natural number. • Apply the module w operation • Domain of X is and will map the same timestamp.

  20. Online Interval Skyline Query Answering • Ex: and w=3 When the base interval becomes

  21. Online Interval Skyline Query Answering • Ex: and w=3 When the base interval becomes

  22. Online Interval Skyline Query Answering • Ex: and w=3 When the base interval becomes = [1,1] and [2,3]

  23. View-Materialization(VM) • Non-redundant skyline time series in interval [i:j] • (1) s is in the skyline interval • (2) s is not in the skyline in any subinterval • Lemma: Give a time series s and an interval if for all interval such that , for any time series then

  24. View-Materialization(VM) • Ex: Compute • Union the non-redundant interval skylines s1=(2,5) s2=(1,5)

  25. SDC 5 4 3 2, 1, 3 2 (4,4) (5,1) (3,2) (5,1) (4,3,2)

  26. Experiment

  27. Conclusion • Interval Skyline Query • Radix priority search tree

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