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Constraint Programming 1. Introduction MapReduced 2. Related Work - - PowerPoint PPT Presentation

Dec 14, 2023 25 likes •226 views

Constraint Programming MapReduced Nikolaos Pothitos, Panagiotis Stamatopoulos Constraint Programming 1. Introduction MapReduced 2. Related Work 3. Our Search Tree Partitioning Schema Nikolaos Pothitos Panagiotis Stamatopoulos

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SLIDE 1

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Constraint Programming MapReduce’d

Nikolaos Pothitos Panagiotis Stamatopoulos

Department of Informatics and Telecommunications National and Kapodistrian University of Athens

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SLIDE 2

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Outline

  • 1. Introduction

◮ MapReduce ◮ Constraint Programming

  • 2. Related Work

◮ Search Tree Partitioning

  • 3. Our Search Tree Partitioning Schema
  • 4. Experiments etc.

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SLIDE 3

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

MapReduce Word-Count Application

◮ We are given a large text ◮ Count each word’s occurrences ◮ Workers

◮ Are either Mappers or Reducers ◮ Distributed or run in parallel 3/20

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SLIDE 4

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

MapReduce Word-Count Application

◮ Each Mapper assigned a text part ◮ Mapper’s output: key, result tuples ◮ Each key, result sent to a Reducer ◮ A Reducer processes all the tuples with the same key

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SLIDE 5

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

MapReduce Word-Count Example

◮ Let the input content be

◮ “design is not just what it looks and it feels like; design

is how it works” ◮ Text distributed to two Mappers

  • 1. “design is not just what it looks and it feels like”
  • 2. “design is how it works”

◮ Mappers’ output (word counters)

  • 1. design, 1, is, 1, not, 1, just, 1, what, 1, it, 2,

looks, 1, and, 1, feels, 1, like, 1.

  • 2. design, 1, is, 1, how, 1, it, 1, works, 1.

◮ Each key corresponds to a Reducer ◮ Two Reducers’ output (word counters)

  • 1. and, 1, design, 2, feels, 1, how, 1, is, 2, it, 3,

just, 1, like, 1, looks, 1.

  • 2. not, 1, what, 1, works, 1.

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SLIDE 6

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Constraint Programming

◮ Constraint Programming includes two phases

  • 1. The Constraint Satisfaction Problem definition
  • 2. The CSP independent solution phase

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SLIDE 7

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Solution Phase

◮ Includes a search tree exploration ◮ Search trees can be huge ◮ Parallelization of exploration is necessary

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SLIDE 8

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Related Work

◮ Work Stealing ◮ SelfSplit ◮ Embarrassingly Parallel Search

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SLIDE 9

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

An Ordinary Search Tree

1 2 13 18 24 3 9 14 19 23 25 31 4 7 10 15 20 26 28 32 34 5 6 8 11 12 16 17 21 22 27 29 30 33 35 36

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SLIDE 10

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

A Top-Down Search Tree Splitting

1 2 13 18 24 3 9 14 19 23 25 31 4 7 10 15 20 26 28 32 34 5 6 8 11 12 16 17 21 22 27 29 30 33 35 36

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SLIDE 11

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Optimum Search Tree Nodes Splitting

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

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SLIDE 12

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Sampling Search Tree Nodes Series

1 2 3 4 5 6 7 8 9 10 13 14 18 21 24 25 26 28 29 30 31

◮ The starred nodes are sampled ◮ Their subtrees are also sampled ◮ We can easily split them ◮ without visiting them all

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SLIDE 13

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Experiments

◮ Cluster creation in the cloud ◮ in ~okeanos GRnet cloud infrastructure ◮ Hadoop installed in eight VMs ◮ One master and seven slaves ◮ VMs equivalent to commodity machines

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SLIDE 14

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

N Queens

◮ Attempt to gather all solutions

◮ 2,279,184 solutions for 15 Queens ◮ 14,772,512 solutions for 16 Queens ◮ 95,815,104 solutions for 17 Queens 14/20

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SLIDE 15

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Speedup for N Queens

4 5 6 7 32 64 128 256 512 15 Queens 9 12 15 18 32 64 128 256 512 16 Queens 8 16 24 32 32 64 128 256 512 17 Queens Speedup Mappers

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SLIDE 16

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Mappers Run Simultaneously

◮ Each machine has eight cores ◮ Each core cannot execute two Mappers simultaneously ◮ At most 64 Mappers run simultaneously ◮ We may spawn more than 64 Mappers

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SLIDE 17

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

N Number Partitioning

◮ Split the set {1, 2, . . . , N} ◮ The two splits are disjoint ◮ with equal cardinality and ◮

  • i∈S1

i =

  • i∈S2

i

◮

  • i∈S1

i2 =

  • i∈S2

i2

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SLIDE 18

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Speedup for N Number Partitioning

4 5 6 7 8 32 64 128 256 512 N =40 Partitioning 10 15 20 25 32 64 128 256 512 N =44 Partitioning 8 16 24 32 40 32 64 128 256 512 N =48 Partitioning Speedup Mappers

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SLIDE 19

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

Conclusions and Future Work

◮ Constraint Programming to MapReduce adaptation ◮ MapReduce parallelization/distribution capabilities

exploitation

◮ Tree sampling vs. top-down splitting ◮ In future, investigate Constraint Optimization ◮ Reducers will gather best solutions

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SLIDE 20

Constraint Programming MapReduce’d Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Our Search

Tree Partitioning Schema

  • 4. Experiments

References

  • J. Dean and S. Ghemawat.

MapReduce: Simplified data processing on large clusters. In OSDI 2004, pages 137–149, 2004. J.-C. R´ egin, M. Rezgui, and A. Malapert. Embarrassingly parallel search. In C. Schulte, editor, CP 2013, volume 8124 of LNCS, pages 596–610. Springer, Berlin Heidelberg, 2013.

  • G. Chu, C. Schulte, and P. J. Stuckey.

Confidence-based work stealing in parallel constraint programming. In I. P. Gent, editor, CP 2009, volume 5732 of LNCS, pages 226–241. Springer, Berlin Heidelberg, 2009.

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