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Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures Klaus-T. Foerster (U. Vienna), Manya Ghobadi (Microsoft Research), Stefan Schmid (U. Vienna) 23 July 2018, IEEE/ACM ANCS 2018 Reconfigurable Data Center

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Klaus-T. Foerster (U. Vienna), Manya Ghobadi (Microsoft Research), Stefan Schmid (U. Vienna)

Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures

23 July 2018, IEEE/ACM ANCS 2018

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SLIDE 2

Page 2 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Reconfigurable Data Center Networks (DCNs)

ProjecToR interconnect Ghobadi et al., SIGCOMM ‘16 Helios (core) Farrington et al., SIGCOMM ‘10 c-Through (HyPaC architecture) Wang et al., SIGCOMM ‘10 Rotornet (rotor switches) Mellette et al., SIGCOMM ‘17 Solstice (architecture & scheduling) Liu et al., CoNEXT ‘15 REACToR Liu et al., NSDI ‘15 … and many more … FireFly Hamedazimi et al., SIGCOMM ‘14

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Page 3 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Reconfigurable Data Center Networks (DCNs)

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Page 3 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Results and conclusions often not portable
  • Between topologies/technologies

Reconfigurable Data Center Networks (DCNs)

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SLIDE 5

Page 3 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Results and conclusions often not portable
  • Between topologies/technologies
  • Assumption in routing takes away optimality

Reconfigurable Data Center Networks (DCNs)

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SLIDE 6

Page 3 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Results and conclusions often not portable
  • Between topologies/technologies
  • Assumption in routing takes away optimality
  • We take a look from a theoretical perspective

Reconfigurable Data Center Networks (DCNs)

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SLIDE 7

Page 3 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Results and conclusions often not portable
  • Between topologies/technologies
  • Assumption in routing takes away optimality
  • We take a look from a theoretical perspective
  • With average path length as an objective

Reconfigurable Data Center Networks (DCNs)

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SLIDE 8

Page 3 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Results and conclusions often not portable
  • Between topologies/technologies
  • Assumption in routing takes away optimality
  • We take a look from a theoretical perspective
  • With average path length as an objective
  • For one switch (with/without this assumption)
  • Also briefly for multiple switches

Reconfigurable Data Center Networks (DCNs)

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Page 4 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

The Static Case

A C E G B D F

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Page 4 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

The Static Case

A C E G B D F Communication frequency: A→E: 10, A→G: 5

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Page 4 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

The Static Case

A C E G B D F Communication frequency: A→E: 10, A→G: 5

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Page 4 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

The Static Case

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70

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Page 5 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70

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SLIDE 14

Page 5 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70

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SLIDE 15

Page 5 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70

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Page 5 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70

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SLIDE 17

Page 5 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70 static Weighted average path length: 1*10+6*5=40 reconfig

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Page 5 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70 static Weighted average path length: 1*10+6*5=40 reconfig

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SLIDE 19

Page 5 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70 static Weighted average path length: 1*10+6*5=40 reconfig 1*10+(1+2)*5=25

  • ptimum
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SLIDE 20

Page 6 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Adding Reconfigurability

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Weighted average path length: 4*10+6*5=70 static Weighted average path length: 1*10+6*5=40 reconfig 1*10+(1+2)*5=25

  • ptimum
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Page 7 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Especially important at scale: multiple reconfigurable switches

Beyond a Single Switch

A Tale of Two Topologies Xia et al., SIGCOMM ‘17 Rotornet Mellette et al., SIGCOMM ‘17

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Page 8 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Segregated Routing Policies

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Page 8 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static

One Switch: Segregated Routing Policies

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SLIDE 24

Page 8 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static

One Switch: Segregated Routing Policies

A C E G B D F Communication frequency: A→E: 10, A→G: 5

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Page 8 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static

One Switch: Segregated Routing Policies

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Why this solution?

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Page 8 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static

One Switch: Segregated Routing Policies

A C E G B D F Communication frequency: A→E: 10, A→G: 5 Why this solution? Benefit of A→E: 10:

  • Static-Reconfig: 40-10=30

Benefit of A→G: 5:

  • Static-Reconfig: 30-5=25
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Page 9 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static

One Switch: Segregated Routing Policies

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Page 9 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static
  • Optimal solution in polynomial time:

One Switch: Segregated Routing Policies

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Page 9 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static
  • Optimal solution in polynomial time:

1. Compute & assign benefit to every matching edge

One Switch: Segregated Routing Policies

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Page 9 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static
  • Optimal solution in polynomial time:

1. Compute & assign benefit to every matching edge 2. Compute optimal weighted matching

One Switch: Segregated Routing Policies

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Page 9 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static
  • Optimal solution in polynomial time:

1. Compute & assign benefit to every matching edge 2. Compute optimal weighted matching

 E.g., weighted Edmond’s Blossom algorithm

One Switch: Segregated Routing Policies

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SLIDE 32

Page 9 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static
  • Optimal solution in polynomial time:

1. Compute & assign benefit to every matching edge 2. Compute optimal weighted matching

 E.g., weighted Edmond’s Blossom algorithm

  • Downside: Only optimal under (artificially!?) segregated routing policy!

One Switch: Segregated Routing Policies

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SLIDE 33

Page 9 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Model: Either just 1 reconfig or just static
  • Optimal solution in polynomial time:

1. Compute & assign benefit to every matching edge 2. Compute optimal weighted matching

 E.g., weighted Edmond’s Blossom algorithm

  • Downside: Only optimal under (artificially!?) segregated routing policy!
  • Not optimal under arbitrary routing policies

One Switch: Segregated Routing Policies

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Page 10 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Non-Segregated Routing

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Page 10 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Non-Segregated Routing

Can improve routing quality

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Page 10 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Non-Segregated Routing

Can improve routing quality NP-hard to optimally compute

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Page 10 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Non-Segregated Routing

Can improve routing quality NP-hard to optimally compute Already for simple settings

(sparse communication patterns, unit weights etc.)

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Page 10 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Non-Segregated Routing

Can improve routing quality NP-hard to optimally compute Already for simple settings

(sparse communication patterns, unit weights etc.)

Approximation algorithms & restricted topologies

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Page 10 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Non-Segregated Routing

Can improve routing quality NP-hard to optimally compute Already for simple settings

(sparse communication patterns, unit weights etc.)

Approximation algorithms & restricted topologies Future Work

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SLIDE 40

Page 10 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

One Switch: Non-Segregated Routing

Can improve routing quality NP-hard to optimally compute Already for simple settings

(sparse communication patterns, unit weights etc.)

Approximation algorithms & restricted topologies Future Work

Already some work in different settings, e.g.:

  • network forms a dynamic tree [Schmid et al., ToN ‘16]
  • constant degree and sparse demands [Avin et al., DISC ‘17]
  • degree depends on node popularity [Avin et al., Inf. Pr. Let. ‘18]

(these works assume all links are reconfigurable)

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Page 11 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Multiple Reconfigurable Switches

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Page 11 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Makes the setting more scalable 

Multiple Reconfigurable Switches

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Page 11 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Makes the setting more scalable 
  • But of course, still NP-hard 

(already for one switch)

Multiple Reconfigurable Switches

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Page 11 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Makes the setting more scalable 
  • But of course, still NP-hard 

(already for one switch)

  • Let’s make things simpler

Multiple Reconfigurable Switches

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Page 12 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Multiple Switches: More than One Flow

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Page 12 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Can we optimize max. path length?

Multiple Switches: More than One Flow

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Page 12 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Can we optimize max. path length?
  • For 2 flows?

Multiple Switches: More than One Flow

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Page 12 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Can we optimize max. path length?
  • For 2 flows?

NP-hard again 

Multiple Switches: More than One Flow

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Page 13 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Multiple Switches: One Flow

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Page 14 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Multiple Switches: One Flow

A C E G B D F Communication frequency: A→G: 1

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Page 14 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

Multiple Switches: One Flow

A C E G B D F Communication frequency: A→G: 1

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Page 14 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Consider weights

Multiple Switches: One Flow

A C E G B D F Communication frequency: A→G: 1

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Page 14 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Consider weights

Multiple Switches: One Flow

A C E G B D F Communication frequency: A→G: 1 5 5 5 5 1 1 10 10 10 10 1 1

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Page 14 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Consider weights

Multiple Switches: One Flow

A C E G B D F Communication frequency: A→G: 1 5 5 5 5 1 1 10 10 10 10 1 1

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Page 14 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • Consider weights

Multiple Switches: One Flow

A C E G B D F Communication frequency: A→G: 1 5 5 5 5 1 1 10 10 10 10 1 1 How to formalize?

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  • Challenge:

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

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  • Challenge:
  • Proper matchings

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

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SLIDE 58
  • Challenge:
  • Proper matchings
  • Polynomial algorithm

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

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SLIDE 59
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

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SLIDE 60
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

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SLIDE 61
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

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SLIDE 62
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

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SLIDE 63
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

Unidirectionality

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SLIDE 64
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

Unidirectionality

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SLIDE 65
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

Unidirectionality

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SLIDE 66
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

Unidirectionality

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SLIDE 67
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

Unidirectionality

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SLIDE 68
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

Unidirectionality

  • Same conceptual idea
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SLIDE 69
  • Challenge:
  • Proper matchings
  • Polynomial algorithm
  • Idea: Use flow algorithms
  • Min-cost integral flow is polynomial

Multiple Switches: One Flow

Page 15 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

A capacity =1

*some small strings attached

Unidirectionality

  • Same conceptual idea

A Aout Ain

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SLIDE 70

Page 16 Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures 23 July 2018

  • one reconfigurable switch
  • segregated: Easy. Not optimal.
  • not seg.: NP-hard. Improves solutions.
  • multiple reconfigurable switches
  • multiple flows: NP-hard
  • just one flow: Easy.
  • Next steps
  • approximation algorithms
  • special topologies

Summary and Outlook

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SLIDE 71

Klaus-T. Foerster (U. Vienna), Manya Ghobadi (Microsoft Research), Stefan Schmid (U. Vienna)

Characterizing the Algorithmic Complexity of Reconfigurable Data Center Architectures

23 July 2018, IEEE/ACM ANCS 2018 Thank you! 