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## PowerPoint Slideshow about ' Online Interval Skyline Queries on Time Series' - paxton

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Online Interval Skyline Query AnsweringOnline Interval Skyline Query AnsweringOnline Interval Skyline Query Answering

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]

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)

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)

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)

- Radix priority search tree

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

- Radix priority search tree

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

- Radix priority search tree

(5,8)

(7,7)

(4,6)

(8,5)

(1,4)

(6,3)

(3,2)

(2,1)

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.

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

Conclusion

- Interval Skyline Query
- Radix priority search tree

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