Power-aware Manhattan routing on chip multiprocessors Anne Benoit 1 - - PowerPoint PPT Presentation

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Power-aware Manhattan routing on chip multiprocessors Anne Benoit 1 - - PowerPoint PPT Presentation

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Framework Theoretical results Heuristics Simulations Power-aware Manhattan routing on chip multiprocessors Anne Benoit 1 , Rami Melhem 2 , Paul Renaud-Goud 1 and Yves Robert 1 , 3 1 . Ecole Normale Sup erieure de Lyon, France, {

slide-1
SLIDE 1

Framework Theoretical results Heuristics Simulations

Power-aware Manhattan routing

  • n chip multiprocessors

Anne Benoit1, Rami Melhem2, Paul Renaud-Goud1 and Yves Robert1,3

  • 1. ´

Ecole Normale Sup´ erieure de Lyon, France, {Anne.Benoit — Paul.Renaud-Goud — Yves.Robert}@ens-lyon.fr

  • 2. University of Pittsburgh, PA, USA, melhem@cs.pitt.edu
  • 3. University of Tennessee Knoxville, TN, USA

Scheduling for Large Scale Systems Workshop June 29, 2012

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 1 / 34

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SLIDE 2

Framework Theoretical results Heuristics Simulations

Motivation and introduction

Power-aware Manhattan routing

  • n chip multiprocessors

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 2 / 34

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SLIDE 3

Framework Theoretical results Heuristics Simulations

Motivation and introduction

Power-aware Manhattan routing

  • n chip multiprocessors

Chip MultiProcessor (CMP): present and future of the processor

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 2 / 34

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SLIDE 4

Framework Theoretical results Heuristics Simulations

Motivation and introduction

Power-aware Manhattan routing

  • n chip multiprocessors

Chip MultiProcessor (CMP): present and future of the processor Manhattan paths into a grid: good value for price

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 2 / 34

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SLIDE 5

Framework Theoretical results Heuristics Simulations

Motivation and introduction

Power-aware Manhattan routing

  • n chip multiprocessors

Chip MultiProcessor (CMP): present and future of the processor Manhattan paths into a grid: good value for price Power issue crucial for both economical and environmental reasons

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 2 / 34

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SLIDE 6

Framework Theoretical results Heuristics Simulations

Motivation and introduction

Power-aware Manhattan routing

  • n chip multiprocessors

Chip MultiProcessor (CMP): present and future of the processor Manhattan paths into a grid: good value for price Power issue crucial for both economical and environmental reasons Scalable links

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 2 / 34

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Framework Theoretical results Heuristics Simulations

Outline of the talk

1

Framework

2

Theoretical results

3

Heuristics

4

Simulations

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 3 / 34

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SLIDE 8

Framework Theoretical results Heuristics Simulations

Outline of the talk

1

Framework

2

Theoretical results

3

Heuristics

4

Simulations

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 4 / 34

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SLIDE 9

Framework Theoretical results Heuristics Simulations

Platform, notations, and power consumption model

Cores arranged onto a 2D grid

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 5 / 34

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SLIDE 10

Framework Theoretical results Heuristics Simulations

Platform, notations, and power consumption model

Cores arranged onto a 2D grid Bi-directional links, but bandwidth not shared among two

  • pposite directions

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 5 / 34

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SLIDE 11

Framework Theoretical results Heuristics Simulations

Platform, notations, and power consumption model

Cores arranged onto a 2D grid Bi-directional links, but bandwidth not shared among two

  • pposite directions

f(u,v)→(u′,v′): fraction of the bandwidth that is used

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 5 / 34

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Framework Theoretical results Heuristics Simulations

Platform, notations, and power consumption model

Cores arranged onto a 2D grid Bi-directional links, but bandwidth not shared among two

  • pposite directions

f(u,v)→(u′,v′): fraction of the bandwidth that is used Pdyn((u, v) → (u′, v′)) = P0 ×

  • f(u,v)→(u′,v′)BW

α, where P0 is a constant and 2 < α ≤ 3 P(u,v)→(u′,v′) = Pleak + P0 ×

  • f(u,v)→(u′,v′)BW

α. If (u, v) → (u′, v′) is inactive, then P(u,v)→(u′,v′) = 0.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 5 / 34

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Framework Theoretical results Heuristics Simulations

Communication model

Communication defined by γi = (Cusrc(i),vsrc(i), Cusnk(i),vsnk(i), δi) Direction di of communication γi Diagonal of cores D(d)

k Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 6 / 34

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Framework Theoretical results Heuristics Simulations

Routing definitions

XY routing (XY): horizontally first, then vertically.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 7 / 34

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SLIDE 15

Framework Theoretical results Heuristics Simulations

Routing definitions

XY routing (XY): horizontally first, then vertically. Single-path Manhattan routing (1-MP): any shortest path

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 7 / 34

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Framework Theoretical results Heuristics Simulations

Routing definitions

XY routing (XY): horizontally first, then vertically. Single-path Manhattan routing (1-MP): any shortest path s-paths Manhattan routing (s-MP): γi can be split into s′ ≤ s distinct communications γi,1, γi,2, . . . , γi,s′, of sizes δi,1, δi,2, . . . , δi,s′

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 7 / 34

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Framework Theoretical results Heuristics Simulations

Routing definitions

XY routing (XY): horizontally first, then vertically. Single-path Manhattan routing (1-MP): any shortest path s-paths Manhattan routing (s-MP): γi can be split into s′ ≤ s distinct communications γi,1, γi,2, . . . , γi,s′, of sizes δi,1, δi,2, . . . , δi,s′ max-paths Manhattan routing (max-MP): special case of s-MP where the number of paths is not bounded. (Remark: actually, there are p+q−2

p−1

  • Manhattan

paths going from C1,1 to Cp,q.)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 7 / 34

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Framework Theoretical results Heuristics Simulations

Problem definition

We are given: a CMP a set of communications {γ1, . . . , γnc } a routing rule (XY or s-MP), with a maximum number s of paths.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 8 / 34

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Framework Theoretical results Heuristics Simulations

Problem definition

We are given: a CMP a set of communications {γ1, . . . , γnc } a routing rule (XY or s-MP), with a maximum number s of paths. Bandwidth must not be exceeded: for all (u, v) ∈ {1, . . . , p} × {1, . . . , q} and Cu′,v′ ∈ succu,v,

  • i ∈ {1, . . . , nc}, j ∈ {1, . . . , s}

(u, v) → (u′, v ′) ∈ pathi,j δi,j ≤ f(u,v)→(u′,v′) × BW .

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 8 / 34

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Framework Theoretical results Heuristics Simulations

Problem definition

We are given: a CMP a set of communications {γ1, . . . , γnc } a routing rule (XY or s-MP), with a maximum number s of paths. Bandwidth must not be exceeded: for all (u, v) ∈ {1, . . . , p} × {1, . . . , q} and Cu′,v′ ∈ succu,v,

  • i ∈ {1, . . . , nc}, j ∈ {1, . . . , s}

(u, v) → (u′, v ′) ∈ pathi,j δi,j ≤ f(u,v)→(u′,v′) × BW . Minimize

  • (u, v) ∈ {1, . . . , p} × {1, . . . , q}

(u′, v ′) ∈ succ(u,v) P(u,v)→(u′,v′)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 8 / 34

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Framework Theoretical results Heuristics Simulations

Quick comparison of routing rules

Pleak = 0, P0 = 1, α = 3, BW = 4 γ1 = (C1,1, C2,2, 1) and γ2 = (C1,1, C2,2, 3).

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 9 / 34

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Framework Theoretical results Heuristics Simulations

Quick comparison of routing rules

Pleak = 0, P0 = 1, α = 3, BW = 4 γ1 = (C1,1, C2,2, 1) and γ2 = (C1,1, C2,2, 3). PXY = 2 × 43 = 128

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 9 / 34

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Framework Theoretical results Heuristics Simulations

Quick comparison of routing rules

Pleak = 0, P0 = 1, α = 3, BW = 4 γ1 = (C1,1, C2,2, 1) and γ2 = (C1,1, C2,2, 3). P1−MP = 2 × (13 + 33) = 56 PXY = 128

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 9 / 34

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Framework Theoretical results Heuristics Simulations

Quick comparison of routing rules

Pleak = 0, P0 = 1, α = 3, BW = 4 γ1 = (C1,1, C2,2, 1) and γ2 = (C1,1, C2,2, 3). P2−MP = 2 × (23 + 23) = 32 PXY = 128 P1−MP = 56

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 9 / 34

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Framework Theoretical results Heuristics Simulations

Outline of the talk

1

Framework

2

Theoretical results

3

Heuristics

4

Simulations

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 10 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

K: sum of all communications K (1)

k : the sum of the γi that cross D(1) k

In this case, K (1)

k

= K for each k

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

K: sum of all communications K (1)

k : the sum of the γi that cross D(1) k

In this case, K (1)

k

= K for each k PXY = (p + q) × K α

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

K: sum of all communications K (1)

k : the sum of the γi that cross D(1) k

In this case, K (1)

k

= K for each k PXY = (p + q) × K α Lower bound on Pmax. Ideal sharing of one communication:

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

Pmax ≥

p−1

  • k=1

2k

  • K (1)

k

2k α +

q−1

  • k=p

(2p − 1)

  • K (1)

k

2p − 1 α +

q+p−2

  • k=q

2(q + p − k − 1)

  • K (1)

k

2(q + p − k − 1) α ,

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

Pmax ≥

p−1

  • k=1

2k

  • K (1)

k

2k α +

q−1

  • k=p

(2p − 1)

  • K (1)

k

2p − 1 α +

q+p−2

  • k=q

2(q + p − k − 1)

  • K (1)

k

2(q + p − k − 1) α , K (1)

k

= K and p−1

k=1 k1−α ≥

p

1 dx/xα−1 Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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SLIDE 32

Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

Pmax ≥

p−1

  • k=1

2k

  • K (1)

k

2k α +

q−1

  • k=p

(2p − 1)

  • K (1)

k

2p − 1 α +

q+p−2

  • k=q

2(q + p − k − 1)

  • K (1)

k

2(q + p − k − 1) α , K (1)

k

= K and p−1

k=1 k1−α ≥

p

1 dx/xα−1, hence

Pmax ≥K α

  • 2×

1 2α−1 1 2 − α

  • 1 − p2−α

+ q − p (2p − 1)α−1

  • .

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(p).

Pmax ≥

p−1

  • k=1

2k

  • K (1)

k

2k α +

q−1

  • k=p

(2p − 1)

  • K (1)

k

2p − 1 α +

q+p−2

  • k=q

2(q + p − k − 1)

  • K (1)

k

2(q + p − k − 1) α , K (1)

k

= K and p−1

k=1 k1−α ≥

p

1 dx/xα−1, hence

Pmax ≥K α

  • 2×

1 2α−1 1 2 − α

  • 1 − p2−α

+ q − p (2p − 1)α−1

  • .

Altogether, Pmax = O(K α) and PXY = O(p × K α), hence the result.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 11 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; single source and destination

Theorem

The upper bound of PXY/Pmax in O(p) is tight.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 12 / 34

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Framework Theoretical results Heuristics Simulations

Manhattan vs XY; multiple sources and destinations

Theorem

Given that q = O(p), an upper bound of PXY/Pmax is in O(pα−1).

Theorem

The upper bound of PXY/Pmax in O(pα−1) can be achieved with a 1-MP routing on a square CMP.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 13 / 34

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Framework Theoretical results Heuristics Simulations

NP-completeness of Manhattan routing

Theorem

Finding a s-MP routing that minimizes the total power consumption while ensuring that link bandwidths are not exceeded is a NP-complete problem.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 14 / 34

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Framework Theoretical results Heuristics Simulations

Outline of the talk

1

Framework

2

Theoretical results

3

Heuristics

4

Simulations

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 15 / 34

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SLIDE 38

Framework Theoretical results Heuristics Simulations

Summary of the heuristics

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 16 / 34

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SLIDE 39

Framework Theoretical results Heuristics Simulations

Summary of the heuristics

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 16 / 34

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SLIDE 40

Framework Theoretical results Heuristics Simulations

Summary of the heuristics

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 16 / 34

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SLIDE 41

Framework Theoretical results Heuristics Simulations

Summary of the heuristics

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends. XY improver (XYI): starts from XY assignment, and moves communications from the highest loaded link.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 16 / 34

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SLIDE 42

Framework Theoretical results Heuristics Simulations

Summary of the heuristics

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends. XY improver (XYI): starts from XY assignment, and moves communications from the highest loaded link. Path remover (PR): virtually pre-assigns communications

  • nto links, and iteratively prevents communications from

using highly loaded links.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 16 / 34

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SLIDE 43

Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends. XY improver (XYI): starts from XY assignment, and moves communications from the highest loaded link. Path remover (PR): virtually pre-assigns communications

  • nto links, and iteratively prevents communications from

using highly loaded links.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 18 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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Framework Theoretical results Heuristics Simulations

Simple greedy (SG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 19 / 34

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SLIDE 56

Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends. XY improver (XYI): starts from XY assignment, and moves communications from the highest loaded link. Path remover (PR): virtually pre-assigns communications

  • nto links, and iteratively prevents communications from

using highly loaded links.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 20 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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Framework Theoretical results Heuristics Simulations

Improved greedy (IG)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 21 / 34

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SLIDE 72

Framework Theoretical results Heuristics Simulations

Two-bend (TB)

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends. XY improver (XYI): starts from XY assignment, and moves communications from the highest loaded link. Path remover (PR): virtually pre-assigns communications

  • nto links, and iteratively prevents communications from

using highly loaded links.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 22 / 34

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Framework Theoretical results Heuristics Simulations

Two-bend (TB)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 23 / 34

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Framework Theoretical results Heuristics Simulations

Two-bend (TB)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 23 / 34

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Framework Theoretical results Heuristics Simulations

Two-bend (TB)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 23 / 34

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends. XY improver (XYI): starts from XY assignment, and moves communications from the highest loaded link. Path remover (PR): virtually pre-assigns communications

  • nto links, and iteratively prevents communications from

using highly loaded links.

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 24 / 34

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 25 / 34

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 25 / 34

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

XY improver (XYI)

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

Simple greedy (SG): greedily assigns communications, hop by hop, on the least loaded link. Improved greedy (IG): virtually pre-assigns communications

  • nto links, then almost like SG.

Two-bend (TB): for each communication, chooses the best path with two bends. XY improver (XYI): starts from XY assignment, and moves communications from the highest loaded link. Path remover (PR): virtually pre-assigns communications

  • nto links, and iteratively prevents communications from

using highly loaded links.

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

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Path remover (PR)

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Framework Theoretical results Heuristics Simulations

Path remover (PR)

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Path remover (PR)

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Path remover (PR)

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Framework Theoretical results Heuristics Simulations

Outline of the talk

1

Framework

2

Theoretical results

3

Heuristics

4

Simulations

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Framework Theoretical results Heuristics Simulations

Simulation settings

8 × 8 CMP Discrete frequencies: 1 Gb/s, 2.5 Gb/s and 3.5 Gb/s Pleak = 16.9 mW, P0 = 5.41 and α = 2.95 Random source and sink nodes for the communications BEST heuristic: best heuristic among all five ones on the given problem instance Each point of the graph: average on 50000 sets of communications

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Framework Theoretical results Heuristics Simulations

Sensitivity to the number of communications

0.2 0.4 0.6 0.8 1 20 40 60 80 100 120 140 Failure ratio Number of communications BEST IG PR XYI XY TB SG

100 Mb/s ≤ δi ≤ 1500 Mb/s

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Framework Theoretical results Heuristics Simulations

Sensitivity to the number of communications

0.2 0.4 0.6 0.8 1 20 40 60 80 100 120 140 Normalized power inverse Number of communications BEST IG PR XYI XY TB SG

100 Mb/s ≤ δi ≤ 1500 Mb/s

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Framework Theoretical results Heuristics Simulations

Sensitivity to the number of communications

0.2 0.4 0.6 0.8 1 10 20 30 40 50 60 70 Normalized power inverse Number of communications BEST IG PR XYI XY TB SG

100 Mb/s ≤ δi ≤ 2500 Mb/s

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Framework Theoretical results Heuristics Simulations

Sensitivity to the number of communications

0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 Normalized power inverse Number of communications BEST IG PR XYI XY TB SG

2500 Mb/s ≤ δi ≤ 3500 Mb/s

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Conclusion

NP-completeness of the problem Minimum upper bound of the ratio of the power consumed by an XY routing over the power consumed by a Manhattan routing Several single-path heuristics: more solutions and less power consumption Future work:

Worst case for single-path Manhattan routing when single source and destination Approximation algorithms Optimal solution for single-path Manhattan routings Multi-path heuristics

Pitt Benoit, Melhem, Renaud, Robert Power-aware Manhattan routing on CMPs 34 / 34