1. ACM Symposium on Parallel Algorithms and
The Push Tree Problem
Frederic Havet, Marc Wennink
ACM Symposium on Parallel Algorithms and
Architectures, 2001
Networks 2004

2. Outline F I n t r o d u c i P b l e m a S O s v T h C H f G R D
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3. Outline F I n t r o d u c i P b l e m a S O s v T h C H f G R D
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4. Introduction I n f o r m a t i d s b u y e g l c p h - . A , v ( ) q
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5. Introduction O n e o f t h m a i r s u g p c - ± y . H w v , d b l T q
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6. Introduction I n g e r a l , m i x t u o f p s h d c b : w k - q . y ¯v
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7. Outline F I n t r o d u c i P b l e m a S O s v T h C H f G R D
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8. Problem Formulation and Some ObservationsG = ( V ) ; E b a n u d i r c g p h , l v
> o f 2 . M H P s T m w q R 8 F y + X
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9. Problem Formulation and Some Observationsh e s o u r c n d t a i p f m g . A v y , - l V ( P ) E q w z R 2 b + F = 1
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10. Problem Formulation and Some Observationsy o h , n p m l u P T r . M v f g q d c S R b - [ k w G N O ( + )
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11. Problem Formulation and Some Observationsc o u l d s a y t h P T r p b m g f S i , . L w = [ v 2 R A I ( ) G
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12. Outline F I n t r o d u c i P b l e m a S O s v T h C H f G R D
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13. The Tree Case V L e t l o a d f n g i s ¸ ( ) = P r . T h u w ¹ 3 c b4 4 4 4 16 s 11 1 4 1 7 1 2 4 2 1 2 2 1 5 5 2 1 2 V 2 e L e t l o a d f n g i s ( ) = P v 2 V r . T h u w 3 c b m p O j E S y q W ; z
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14. Outline F I n t r o d u c i P b l e m a S O s v T h C H f G R D
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15. Heuristics For The General CaseW e h a v l r d y k n o w t p i m s u P T b . g c , f
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16. Heuristics For The General CaseP r o p s i t n 1 F a y
> , h e x c f u T b l m w ( S ) W d s = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 u H e r , w ( S P T t h g n l i ) = b u a c k 1 +
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17. Heuristics For The General CaseP r o p s i t n 2 F a y
> , h e x c f u T b l m w ( M S ) W g s 1 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 1 1 1 1 1 1 1 H e r , w ( M S T t h g n l i ) = b u d 1 +
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18. Heuristics For The General Casem 1 C n s i d a t c f P u p b l w ( z ) q = v 2 R , L x + - S . ; g
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19. Outline F I n t r o d u c i P b l e m a S O s v T h C H f G R D
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20. Robustness S u p o s e t h a w v b i n d r g l m - f c q . H y ¯ ? W ®, R
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21. Robustness Increasing and Decreasing Requests Almost UniformlyP r o p s i t n 3 L e 1 a d l ; b w q u f c h ( v ) 2 R . F y g , T = m C x S V G
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22. Robustness Increasing and Decreasing Requests Almost UniformlyW e n o w p r v t h f l i g m a s d - x P u T b q c ; . 2 C L
< 1 , ( ) + 8 R = : B
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23. Robustness Adding Requests
Robustness Adding Requests s 1 k P r o p s i t n 4 F a y 1 , h e x c f u T b l m w q d g ; ( )
> v = . L k 2 3 C G : +
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24. Robustness Removing Requests1 1 1
M-1 u w v
1/0 1 P r o p s i t n 5 F a y
> , h e x c f u T b l m w q d g ( ) 1 + ; M v = . C N W
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25. Robustness Removing Requestsc e h a b v p r s n l y d f
> . T u - m w g ( = ) 3 C P x q W , ;
< L H z
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26. Outline F I n t r o d u c i P b l e m a S O s v T h C H f G R D
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27. Discussion W e m a y c o n s i d r l t f : F h k g p u T v b q - P A ,
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