Loading in 5 sec....

A Deterministic Algorithm for Summarizing Asynchronous Streams over a Sliding WindowPowerPoint Presentation

A Deterministic Algorithm for Summarizing Asynchronous Streams over a Sliding Window

- By
**deva** - Follow User

- 126 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' A Deterministic Algorithm for Summarizing Asynchronous Streams over a Sliding Window' - deva

**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

### A Deterministic Algorithm forSummarizing Asynchronous Streamsover a Sliding Window

Costas Busch

Rensselaer Polytechnic Institute

Srikanta Tirthapura

Iowa State University

Most recent time window of duration

Current

time

Data stream:

Goal:

Compute the sum of elements with

time stamps in time window

- Example I: All packets on a network link, maintain the number of different ip sources in the last one hour
- Example II: Large database, continuously maintain averages and frequency moments

- Synchronous stream
- ti: In ascending order

- Asynchronous stream
- ti: No order guaranteed

Data stream:

Why Asynchronous Data Streams?

Synchronous stream

Asynchronous stream

Network delay & multi-path routing

Synchronous

Asynchronous

Synchronous

Merge w/o control

- Processing Requirements:
- One pass processing
- Small workspace: poly-logarithmic in the size of data
- Fast processing time per element
- Approximate answers are ok

[Datar, Gionis, Indyk, Motwani.

SIAM Journal on Computing, 2002]

Deterministic, Synchronous

Merging buckets

[Tirthapura, Xu, Busch, PODC, 2006]

Randomized, Asynchronous

Random sampling

Most recent time window of duration

Current

time

Data stream:

Goal:

Compute the sum of elements with

time stamps in time window

Data structure consists of various levels

is an upper bound of the sum in a period

Increase counter value

Increase counter value

Increase counter value

Increase counter value

New buckets have threshold also

Increase appropriate bucket

Increase appropriate bucket

Increase appropriate bucket

Split bucket

Increase appropriate bucket

Split bucket

Suppose we want to find the sum

of elements in time period

of splitting threshold

First level with a leaf bucket

that intersects timeline

Consider buckets on right of timeline

in order to compute the estimate

:elements of left part counted on right

:elements of right part counted on left

It can be proven

Download Presentation

Connecting to Server..