Online Interval Skyline Queries on Time Series

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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

Outline
• Introduction
• Interval Skyline Query
• Algorithm
• On-The-Fly (OTF)
• View-Materialization(VM)
• Experiment
• Conclusion
Introduction
• A power supplier need to analyze the consumption of different regions in the service area.
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]
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.

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 .

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]

(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]

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

View-Materialization(VM)
• Ex: Compute
• Union the non-redundant

interval skylines

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

SDC

5 4

3

2, 1, 3

2

(4,4)

(5,1)

(3,2)

(5,1)

(4,3,2)

Conclusion
• Interval Skyline Query