Loading in 5 sec....

Online Interval Skyline Queries on Time SeriesPowerPoint Presentation

Online Interval Skyline Queries on Time Series

- 133 Views
- Uploaded on

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

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Online Interval Skyline Queries on Time Series

Online Interval Skyline Query Answering

Online Interval Skyline Query Answering

Online Interval Skyline Query Answering

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]

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

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.

Online Interval Skyline Query Answering

- Ex: and w=3
When the base interval becomes

Online Interval Skyline Query Answering

- Ex: and w=3
When the base interval becomes

Online Interval Skyline Query Answering

- 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)

- Union the non-redundant

Conclusion

- Interval Skyline Query
- Radix priority search tree

Download Presentation

Connecting to Server..