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# Online Interval Skyline Queries on Time Series - PowerPoint PPT Presentation

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

ICDE 2009

• Introduction

• Interval Skyline Query

• Algorithm

• On-The-Fly (OTF)

• View-Materialization(VM)

• Experiment

• Conclusion

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

• 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]

• 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.

• 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 .

Iteravively process the time series in S in their max value descending order

Ex:

Consider

Let usCompute the skyline in interval [2,3]

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

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

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

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

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

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

• 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.

• Ex: and w=3

When the base interval becomes

• Ex: and w=3

When the base interval becomes

• Ex: and w=3

When the base interval becomes

=

[1,1] and [2,3]

• 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

• Ex: Compute

• Union the non-redundant

interval skylines

s1=(2,5) s2=(1,5)

5 4

3

2, 1, 3

2

(4,4)

(5,1)

(3,2)

(5,1)

(4,3,2)

• Interval Skyline Query