Computing Bottom SCCs Symbolically Using Transition Guided Reduction

Nikola Beneš, Luboš Brim, Samuel Pastva, and David Šafránek

bottom strongly connected components

bottom SCC Algorithms

"Optimal" Symbolic Algorithm

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Pivot Vertex ⇒ 

"Optimal" Symbolic Algorithm

Backward set (B) ⇒ 

Pivot Vertex ⇒ 

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"Optimal" Symbolic Algorithm

Backward set (B) ⇒ 

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Forward set (F) ⇒ 

"Optimal" Symbolic Algorithm

Backward set (B) ⇒ 

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Forward set (F) ⇒ 

Not a bottom SCC

"Optimal" Symbolic Algorithm

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×

⇐ Pivot Vertex  

Large SCC are sometimes small

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10^30

10^10

0.000000000000000001%

Poor Pivot Selection

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×

×

×

×

×

×

×

×

BASIN DIAMETER

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y

x

x << y

Interleaved Transition Guided Reduction (ITGR)

ITGR: Goal

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×

ITGR: Goal

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⇐ Pivot  Set

ITGR: Goal

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Backward set (B) 

ITGR: Goal

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Backward set (B) 

Forward Set 
(F) 

ITGR: Goal

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Backward set (B) 

Forward Set 
(F) 

ITGR: Goal

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Backward set (B) 

Forward Set 
(F) 

Is it any good?

ITGR: EVALUATION

125 real models, 200 randomly generated