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

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 2019/4/25

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 2019/4/25

Introduction I n f o r m a t i d s b u y e g l c p h - . A , v ( ) q 2019/4/25

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 2019/4/25

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 ± 2019/4/25

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 2019/4/25

Problem Formulation and Some Observations G = ( 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 ¹ ¸ q R µ 8 F y + X 2019/4/25

Problem Formulation and Some Observations h e s o u r c n d t a i p f m g ¹ . A v y , - l V ( P ) E ± q w z R 2 b + F = 1 2019/4/25

Problem Formulation and Some Observations y o h , n p m l u P T r . M v f g q d ± c ¯ S ¹ R b - [ k w G N O ( + ) 2019/4/25

Problem Formulation and Some Observations c o u l d s a y t h P T r p b m g f S i , ¹ . L w = [ v 2 R A ¯ ± I ( ) G 2019/4/25

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 2019/4/25

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 b 4 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 ¹ 3 c b m p O j E S ¯ y q W ; ± z 2019/4/25

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 2019/4/25

Heuristics For The General Case W e h a v l r d y k n o w t p i m s u P T b . g c , ¤ f ± 2019/4/25

Heuristics For The General Case P r o p s i t n 1 F a y ½ > , 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 1 ² ² ² ² ² ² ² ² u H e r , w ( S P T t h g n l i ) = b u ¤ a c k 1 + ² 2019/4/25

Heuristics For The General Case P r o p s i t n 2 F a y ½ > , h e x c f u T b l m w ( M S ) ¤ W g s 1 1 + ² 1 + ² 1 + ² 1 + ² 1 + ² 1 + ² 1 + ² 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 + ² 2019/4/25

Heuristics For The General Case m 1 C n s i d a t c f P u p b l w ¹ ( z ) q = v 2 R , L x + - S ½ . ¤ · £ ; ¸ g 2019/4/25

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 2019/4/25

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 2019/4/25

Robustness Increasing and Decreasing Requests Almost Uniformly P 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 ¹ C x S V G ¤ 2019/4/25

Robustness Increasing and Decreasing Requests Almost Uniformly W 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 · ² » < 1 , ( ¡ ) + 8 R ½ ¸ ¤ = : B 2019/4/25

Robustness Adding Requests ± Robustness Adding Requests s 1 k P r o p s i t n 4 F a y ½ ¸ 1 , h e x c f u T b l m w q d g ; ( ) ¤ > v = ¹ . L k 2 ± 3 C G : + · 2019/4/25

Robustness Removing Requests ¡ 1 ± 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 2019/4/25

Robustness Removing Requests c 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 · ¡ ¹ ¤ H z 2019/4/25

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 2019/4/25

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 , 2019/4/25