Prioritized Restreaming Algorithms for Balanced Graph Partitioning - - PowerPoint PPT Presentation

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Prioritized Restreaming Algorithms for Balanced Graph Partitioning - - PowerPoint PPT Presentation

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Prioritized Restreaming Algorithms for Balanced Graph Partitioning Amel Awadelkarim ameloa@stanford.edu Johan Ugander jugander@stanford.edu Balanced graph partitioning We want to partition a graph into node-sets of approximately equal size,

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SLIDE 1

Prioritized Restreaming Algorithms for Balanced Graph Partitioning

Amel Awadelkarim

ameloa@stanford.edu

Johan Ugander

jugander@stanford.edu

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SLIDE 2

We want to partition a graph into node-sets of approximately equal size, while minimizing the number of edges cut.

Balanced graph partitioning

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 1

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SLIDE 3

This problem has practical application as an imperative step for large-scale distributed graph computation.

Balanced graph partitioning

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 2

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SLIDE 4

The exact solution is infeasible to compute, hence we focus on iterative local heuristics. Global Multilevel Local

Existing algorithms

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 3

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SLIDE 5

The exact solution is infeasible to compute, hence we focus on iterative local heuristics. Global Multilevel Local

Existing algorithms

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 4

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SLIDE 6

Specifically, we explore the role of stream order in (re)streaming algorithms and introduce prioritized restreaming algorithms. Global

Streaming Prioritized

Multilevel Local

A new class of algorithms

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 5

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SLIDE 7
  • 1. A taxonomy of existing iterative techniques
  • 2. Informative benchmarking that was absent

from the literature

  • 3. A paradigm shift in restreaming partitioning

algorithms

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 6

Contributions

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SLIDE 8

Existing methods Taxonomy Prioritized restreaming Results

  • Benchmark existing methods
  • Prioritized restreaming results
  • Correlation between stream orders

Outline

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 7

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SLIDE 9

Existing methods Taxonomy Prioritized restreaming Results

  • Benchmark existing methods
  • Prioritized restreaming results
  • Correlation between stream orders

Outline

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 8

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SLIDE 10

Existing methods Taxonomy Prioritized restreaming Results

  • Benchmark existing methods
  • Prioritized restreaming results
  • Correlation between stream orders

Outline

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 9

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SLIDE 11

Existing methods Taxonomy Prioritized restreaming Results

  • Benchmark existing methods
  • Prioritized restreaming results
  • Correlation between stream orders

Outline

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 10

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SLIDE 12

Existing methods

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 11

We present three algorithms from the literature – two based on label propagation and one restreaming algorithm.

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SLIDE 13

BLP begins from an initial partitioning, iteratively improving upon the edge cut objective.

V1 V2 V3

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 12

Balanced label propagation

Ugander and Backstrom. WSDM. 2013.

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SLIDE 14

At each iteration, BLP identifies which nodes desire to move and to where,

V1 V2 V3

Balanced label propagation

Ugander and Backstrom. WSDM. 2013.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 13

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SLIDE 15

places nodes in sorted move queues to their target shards by order of decreasing gain,

gu = max

i∈[k] Nu,i − Nu,P (u)

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Neighbors in shard i Neighbors in current shard assignment, P(u)

Balanced label propagation

Ugander and Backstrom. WSDM. 2013.

Gain of node u

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 14

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SLIDE 16

then solves a linear program to determine how many top nodes to relocate.

V1 V2 V3

Balanced label propagation

Ugander and Backstrom. WSDM. 2013.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 15

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SLIDE 17

V1 V2 V3

Balanced label propagation

Ugander and Backstrom. WSDM. 2013.

then solves a linear program to determine how many top nodes to relocate.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 16

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SLIDE 18

V1 V2 V3

Balanced label propagation

Ugander and Backstrom. WSDM. 2013.

then solves a linear program to determine how many top nodes to relocate.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 17

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SLIDE 19

SHP also starts from an initial partitioning.

V1 V2 V3

Social Hash partitioner

Kabiljo et al. VLDB. 2017.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 18

Shalita et al. NSDI. 2016.

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SLIDE 20

At each iteration, we place all nodes in the move queue of the shard that maximizes a modified form of gain,

V1 V2 V3

Social Hash partitioner

Kabiljo et al. VLDB. 2017.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 19

Shalita et al. NSDI. 2016.

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SLIDE 21

g0

u =

max

i2[k]\P (u) Nu,i − Nu,P (u)

<latexit sha1_base64="S53pKRdZUXcmEJCT5lRYHr+o24=">ACInicbZDLSsNAFIYn3q23qEs3gyIqaEnqwgsIXjaupIJVoQlhMp2Q2cmcS5iCXkWNz6Cr+DGhaKuB/GaePC2w8DH/85hzPnj1NGlfa8d2dgcGh4ZHRsvDQxOTU9487OnavESExqOGJvIyRIowKUtNUM3KZSoJ4zMhF3Dnq1S+uiVQ0EWe6m5KQo5agTYqRtlbk7rRWIgP3YMDRTZTRgIp6JwU0ZwKo2B1azl8CTKzDrN4UZBhRu5S17Z6wv+Bf8LlvYP8qujnd37auS+Bo0EG06ExgwpVfe9VIcZkpiRvJSYBRJEe6gFqlbFIgTFWb9E3O4bJ0GbCbSPqFh3/0+kSGuVJfHtpMj3Va/az3zv1rd6OZ2mFGRGk0ELhY1DYM6gb28YINKgjXrWkBYUvtXiNtIqxtqiUbgv/75L9wXin7m+XKqU3jEBQaAwtgEawCH2yBfXAMqAGMLgFD+AJPDt3zqPz4rwVrQPO18w8+CHn4xMjnqUX</latexit>

the max gain outside of a node’s current shard assignment, and sort move queues by this quantity.

Max over external shards

Social Hash partitioner

Kabiljo et al. VLDB. 2017.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 20

Shalita et al. NSDI. 2016.

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SLIDE 22

V1 V2 V3

Balance is maintained by swapping nodes between shard pairs, only doing so when the net gain is positive.

Social Hash partitioner

Kabiljo et al. VLDB. 2017.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 21

Shalita et al. NSDI. 2016.

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SLIDE 23

V1 V2 V3

Social Hash partitioner

Kabiljo et al. VLDB. 2017.

Balance is maintained by swapping nodes between shard pairs, only doing so when the net gain is positive.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 22

Shalita et al. NSDI. 2016.

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SLIDE 24

V1 V2 V3

Social Hash partitioner

Kabiljo et al. VLDB. 2017.

Balance is maintained by swapping nodes between shard pairs, only doing so when the net gain is positive.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 23

Shalita et al. NSDI. 2016.

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SLIDE 25

V1 V2 V3

Social Hash partitioner

Kabiljo et al. VLDB. 2017.

The SHP algorithm boasts many bells and whistles. We denote this version KL-SHP and also study two restricted forms, SHP-I and SHP-II.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 24

Shalita et al. NSDI. 2016.

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SLIDE 26

ReLDG is a streaming algorithm, and does not require an initial partitioning.

V1 V2 V3

Restreaming linear deterministic greedy

Nishimura and Ugander. KDD. 2013.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 25

Stanton and Kliot. KDD. 2012.

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SLIDE 27

It repeatedly streams nodes one at a time to the shard that satisfies the given assignment mechanism.

V1 V2 V3

Restreaming linear deterministic greedy

Nishimura and Ugander. KDD. 2013.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 26

Stanton and Kliot. KDD. 2012.

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SLIDE 28

It repeatedly streams nodes one at a time to the shard that satisfies the given assignment mechanism.

V1 V2 V3

Restreaming linear deterministic greedy

Nishimura and Ugander. KDD. 2013.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 27

Stanton and Kliot. KDD. 2012.

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SLIDE 29

arg max

i∈[k] |V (t) i

∩ N(u)| · 1 − x(t)

i

C !

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Restreaming linear deterministic greedy

Nishimura and Ugander. KDD. 2013.

It repeatedly streams nodes one at a time to the shard that satisfies the given assignment mechanism.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 28

Stanton and Kliot. KDD. 2012.

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SLIDE 30

arg max

i∈[k] |V (t) i

∩ N(u)| · 1 − x(t)

i

C !

<latexit sha1_base64="vkqNJM75D5iuHXH2/jeh+gMRBGw=">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</latexit>

Share of u’s neighbors in shard i, Nu,i

Restreaming linear deterministic greedy

Nishimura and Ugander. KDD. 2013.

It repeatedly streams nodes one at a time to the shard that satisfies the given assignment mechanism.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 29

Stanton and Kliot. KDD. 2012.

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SLIDE 31

arg max

i∈[k] |V (t) i

∩ N(u)| · 1 − x(t)

i

C !

<latexit sha1_base64="vkqNJM75D5iuHXH2/jeh+gMRBGw=">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</latexit>

Restreaming linear deterministic greedy

Nishimura and Ugander. KDD. 2013.

It repeatedly streams nodes one at a time to the shard that satisfies the given assignment mechanism.

Multiplicative weight on emptiness of shard i

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 30

Stanton and Kliot. KDD. 2012.

Share of u’s neighbors in shard i, Nu,i

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SLIDE 32

BLP KL-SHP reLDG Reassignment mechanism Synchronous Synchronous Streaming Constraint handling Flow-based (LP) Pairwise (swaps) Multiplicative weight Incumbency Priority

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 31

Algorithmic taxonomy

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SLIDE 33

BLP KL-SHP reLDG Reassignment mechanism Synchronous Synchronous Streaming Constraint handling Flow-based (LP) Pairwise (swaps) Multiplicative weight Incumbency Priority

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 32

Algorithmic taxonomy

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SLIDE 34

BLP KL-SHP reLDG Reassignment mechanism Synchronous Synchronous Streaming Constraint handling Flow-based (LP) Pairwise (swaps) Multiplicative weight Incumbency Priority

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 33

Algorithmic taxonomy

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SLIDE 35

BLP KL-SHP reLDG Reassignment mechanism Synchronous Synchronous Streaming Constraint handling Flow-based (LP) Pairwise (swaps) Multiplicative weight Incumbency Priority

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 34

Algorithmic taxonomy

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SLIDE 36

BLP KL-SHP reLDG Reassignment mechanism Synchronous Synchronous Streaming Constraint handling Flow-based (LP) Pairwise (swaps) Multiplicative weight Incumbency Priority

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 35

Algorithmic taxonomy

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SLIDE 37

BLP KL-SHP reLDG Reassignment mechanism Synchronous Synchronous Streaming Constraint handling Flow-based (LP) Pairwise (swaps) Multiplicative weight Incumbency Priority

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 36

Algorithmic taxonomy

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SLIDE 38

The order in which we choose to stream nodes is an

  • bvious avenue for injecting priority into reLDG.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 37

Priority in stream order

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SLIDE 39

So far, only random, BFS and DFS (from a random node) orders are discussed in the literature.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 38

Priority in stream order

Previously studied orders Random BFS/DFS (from random node)

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SLIDE 40

In the offline setting, we can choose more strategic static and dynamic orderings.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 39

Priority in stream order

Prioritized orders BFS (from highest degree) Local clustering coefficient Degree Gain, gu

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SLIDE 41

In the offline setting, we can choose more strategic static and dynamic orderings.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 40

Priority in stream order

Prioritized orders BFS (from highest degree) Local clustering coefficient Degree Gain, gu Ambivalence, au

slide-42
SLIDE 42

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 41

New metric for sorting order

au = − max

i∈[k]\P (u) |Nu,i − Nu,P (u)|

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Ambivalence of node u

slide-43
SLIDE 43

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 42

New metric for sorting order

au = − max

i∈[k]\P (u) |Nu,i − Nu,P (u)|

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Ambivalence of node u Negative max over external shards

slide-44
SLIDE 44

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 43

New metric for sorting order

au = − max

i∈[k]\P (u) |Nu,i − Nu,P (u)|

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Ambivalence of node u Negative max over external shards Absolute difference in co-located neighbor count

slide-45
SLIDE 45

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 44

The larger the magnitude of the difference, the more negative the value, the less “ambivalent” the node is to relocation.

New metric for sorting order

au = − max

i∈[k]\P (u) |Nu,i − Nu,P (u)|

<latexit sha1_base64="L3X7W0PfYMSJ9j/JM2sVK6mPC64=">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</latexit>

Ambivalence of node u Negative max over external shards Absolute difference in co-located neighbor count

slide-46
SLIDE 46

First, we plot internal edge fraction of BLP, KL-SHP, and reLDG as a function of iteration on 4 datasets.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 45

Benchmarking base methods

slide-47
SLIDE 47

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 46

BLP and KL-SHP display similar performance, with KL-SHP winning out on all tested networks.

Benchmarking base methods

slide-48
SLIDE 48

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 47

reLDG with random stream order results in higher quality partitions in fewer iterations than both synchronous ones.

Benchmarking base methods

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SLIDE 49

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 48

To investigate the assignment behavior of nodes under our three base methods, we plot their periodicity.

Periodic reassignment of synchronous class

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SLIDE 50

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 49

We find that many nodes get assigned to the shard they were assigned to two iterations prior under the synchronous algorithms.

Periodic reassignment of synchronous class

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SLIDE 51

Synchronous:

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 50

The phenomenon is illustrated well by a bipartite network and provides intuition for streaming’s superior performance.

Periodic reassignment of synchronous class

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SLIDE 52

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 51

Synchronous:

Periodic reassignment of synchronous class

The phenomenon is illustrated well by a bipartite network and provides intuition for streaming’s superior performance.

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SLIDE 53

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 52

Synchronous:

Periodic reassignment of synchronous class

The phenomenon is illustrated well by a bipartite network and provides intuition for streaming’s superior performance.

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SLIDE 54

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 53

Synchronous: Streaming:

… Periodic reassignment of synchronous class

The phenomenon is illustrated well by a bipartite network and provides intuition for streaming’s superior performance.

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SLIDE 55

Synchronous vs. streaming performance

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 54

Internal edge fraction of 16-shard partitioning after 10 iterations, averaged over 10 trials.

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SLIDE 56

Synchronous vs. streaming performance

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 55

Internal edge fraction of 16-shard partitioning after 10 iterations, averaged over 10 trials.

Best

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SLIDE 57

Synchronous vs. streaming performance

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 56

Internal edge fraction of 16-shard partitioning after 10 iterations, averaged over 10 trials.

Worst

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SLIDE 58

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 57

Note that the worst performing stream order outperforms the best performer of the synchronous class, a truly remarkable result.

Internal edge fraction of 16-shard partitioning after 10 iterations, averaged over 10 trials.

Synchronous vs. streaming performance

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SLIDE 59

Prioritized restreaming

Furthermore, streaming nodes in order of increasing ambivalence can significantly improve the quality of the resulting partition.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 58

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SLIDE 60

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 59

Furthermore, streaming nodes in order of increasing ambivalence can significantly improve the quality of the resulting partition.

Prioritized restreaming

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SLIDE 61

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 60

Prioritized restreaming

Internal edge fraction of 16-shard partitioning after 10 iterations, averaged over 10 trials.

Prioritized orders

The top performer in each row lies in the prioritized restreaming category, showing up to 12% improvement in objective from random.

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SLIDE 62

Correlation between stream orders

To quantify their differences, we plot the weighted Kendall’s tau correlation between all tested stream orders.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 61

  • Vigna. WWW. 2015.
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SLIDE 63

Decreasing-degree and increasing-ambivalence are highly correlated orderings.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 62

Correlation between stream orders

  • Vigna. WWW. 2015.
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SLIDE 64

Further, ambivalence is upper and lower bounded by a linear function of degree, relative to a random partitioning.

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 63

2 k · du ≤ E[˜ au] ≤ 2(k − 1) k · du

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Ambivalence and degree

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SLIDE 65

Takeaways

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 64

From this talk

Streaming > synchronous. Prioritized orders show significant improvement over random. Ambivalence and degree are most promising

  • rders and are highly correlated.
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SLIDE 66

Takeaways

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 65

From paper

“Less is more” within synchronous. Incumbency exploration shows that methods are good as is regarding the option. reLDG outperforms previously benchmarked methods with increasing k.

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SLIDE 67

Thank you!

Awadelkarim and Ugander Prioritized Restreaming Algorithms for Balanced Graph Partitioning 66

Awadelkarim and Ugander. “Prioritized Restreaming Algorithms for Balanced Graph Partitioning”.