Sketching, Sampling, and other Sublinear Algorithms 4 (Lecture by Alex Andoni)
Upcoming SlideShare
Loading in...5
×
 

Sketching, Sampling, and other Sublinear Algorithms 4 (Lecture by Alex Andoni)

on

  • 695 views

Parallel framework: we look at problems where neither the data or the output fits on a machine. For example, given a set of 2D points, how can we compute the minimum spanning tree over a cluster of ...

Parallel framework: we look at problems where neither the data or the output fits on a machine. For example, given a set of 2D points, how can we compute the minimum spanning tree over a cluster of machines.

Statistics

Views

Total Views
695
Views on SlideShare
321
Embed Views
374

Actions

Likes
0
Downloads
2
Comments
0

2 Embeds 374

http://almada2013.ru 373
http://cloud2014.cs.msu.ru 1

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment
  • Machines churning data
  • pictures of problems!

Sketching, Sampling, and other Sublinear Algorithms 4 (Lecture by Alex Andoni) Sketching, Sampling, and other Sublinear Algorithms 4 (Lecture by Alex Andoni) Presentation Transcript

  • Sketching, Sampling and other Sublinear Algorithms: Algorithms for parallel models Alex Andoni (MSR SVC)
  • Parallel Models  Data cannot be seen by one machine  Distributed across many machines  MapReduce, Hadoop, Dryad,…  Algorithmic tools for the models?  very incipient!
  • Types of problems  0. Statistics: 2nd moment of the frequency  1. Sort n numbers  2. s-t connectivity in a graph  3. Minimum Spanning Tree on a graph  … many more!
  • Computational Model 
  • Model Constraints 
  • PRAMs 
  • Problem 0: Statistics  IP 2 1 5 3 7 2 1 9 4
  • Problem 1: sorting 
  • Problem 2: graph connectivity  VS
  • Problems 3: geometric graphs 
  • Problem: Geometric MST  [A-Nikolov-Onak-Yaroslavtsev’??]
  • General Approach  Partition the space hierarchically in a “nice way”  In each part  Compute a pseudo-solution to the problem  Sketch the pseudo-solution with small space  Send the sketch to be used in the next level/round
  • MST algorithm: attempt 1  Partition the space hierarchically in a “nice way”  In each part  Compute a pseudo-solution to the problem  Sketch the pseudo-solution with small space  Send the sketch to be used in the next level/round quad trees! compute MST send any point as a representative
  • Troubles  Quad tree can cut MST edges  forcing irrevocable decisions  Choose a wrong representative
  • MST algorithm: final 
  • MST algorithm: Glimpse of analysis 
  • Finale  Gotta love your models:  Streaming:  sub-linear space  see all data sequentially  Parallel computing:  sub-linear space per machine  data distributed over many machines  communication (rounds) expensive  Algorithmic tools in development!