Fence-Insertion for Structured Programs Arash Pourdamghani - PowerPoint PPT Presentation

Fence-Insertion for Structured Programs Arash Pourdamghani Mohammad Taheri Mohsen Lesani Spring 2020 University of Vienna

Developing a Distributed System! 2

Looking Deeper 357 F(x) ……….. 385 F’(x) 3

Out of Order Execution F’(x) 357 F(x) ↓ ……….. 385 F’(x) F(x) Programmer's Runtime 4 Expectation Execution

Fence Insertion 500 H(x) 357 F(x) 525 H’(x) 385 F’(x) 146 G(x) 912 G’(x) 5

Our Solution 6

Outline Problem Poly-time NP-Hardness Statement Algorithm 7

CFG 8

A Closer Look h F(x) i Some Code k G(x) 9

Maintaining Correctness h F(x) i Some Code k F’(x) 10

Fence Insertion h F(x) i Some Code k F’(x) 11

All Constraints 12

Naive Solution 13

Optimization 14

Outline Problem Poly-time NP-Hardness Statement Algorithm 15

Reduction from Minimum Set Cover 𝑉 = 𝑣 1 , 𝑣 2 , 𝑣 3 , 𝑣 4 , … , u n 𝑇 = 𝑇 1 , 𝑇 2 , … , 𝑇 𝑛 𝐹𝑦𝑏𝑛𝑞𝑚𝑓: 𝑇1 = 𝑣 1 , 𝑣 2 , 𝑣 3 , 𝑇2 = {𝑣 2 , 𝑣 4 } 16

Reduction from Minimum Set Cover 𝑉 = 𝑣 1 , 𝑣 2 , 𝑣 3 , 𝑣 4 , … , u n : Constraint Types, Straight line program with 2n instructions, Constraints with type 𝑣 𝑗 𝑝𝑜 𝑤 𝑗 , 𝑤 2𝑜−𝑗+1 , 2 + 1): The middle edge (𝑤 𝑜 2 , 𝑤 𝑜 17

Reduction from Minimum Set Cover 𝑇 = 𝑇 1 , 𝑇 2 , … : Fence Types We could many fences of 𝑇 𝑗 𝐹𝑦𝑏𝑛𝑞𝑚𝑓: 𝑇1 = 𝑣 1 , 𝑣 2 , 𝑣 3 , 𝑇2 = {𝑣 2 , 𝑣 4 } 18

Given Solution of Fence Insertion 𝑉 = 𝑣 1 , 𝑣 2 , 𝑣 3 , 𝑣 4 , … 𝑇 = {𝑇 1 , 𝑇 2 , … } 19

Given Solution of Minimum Set Cover 𝑉 = 𝑉 1 , 𝑉 2 , 𝑉 3 , 𝑉 4 , … 𝑇 = {𝑇 1 , 𝑇 2 , … } 20

Outline Problem Poly-time NP-Hardness Statement Algorithm 21

P 22

Algorithm Overview 1- Constraint Elimination 2- Finding Diamond 3- Decomposing into Paths 4- Solving for Paths 23

Out of Order Execution! 4- Solving for Paths 1- Constraint Elimination 2- Finding Diamond 2- Finding Diamond 1- Constraint Elimination 3- Decomposing into Paths 3- Decomposing into Paths 4- Solving for Paths 24

A Simple Path 25

A Simple Path 26

A Simple Path 27

A Simple Path 28

A Simple Path 29

Structured 30

A(C)FG 31

Finding Diamonds 32

Level 0 33

Level 1 34

Level 2 35

Branch/Merge 36

Algorithm 37

Algorithm 38

Fence Elimination 39

Passing Constraints 40

Spanning Constraints 41

Control Dependency Preservation 42

Decomposing into simple paths 43

Absorption in a Path 44

Emission in a Path 45

Before 46

After Level 0 47

After Level 1 48

The End! 49

Complexity 1- 𝐹 ∈ 𝑃 𝑊 2-Elimination: 𝑃 𝐷 + 𝑊 3-Finding Diamonds: 𝑃 𝑊𝑚𝑝𝑕𝑊 4-Decompsiton and Insertion: σ |𝑞| |𝐷 𝑞 𝑗 |𝑚𝑝𝑕𝐷 𝑞 𝑗 + |𝑊 𝑞𝑗 | ⇒ Polynomial Time! 50

What about loops? 51

Elimination 52

Transformation 53

Thank you 54

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