performance and energy optimization of concurrent
play

Performance and energy optimization of concurrent pipelined - PowerPoint PPT Presentation

Aug 13, 2022 •144 likes •1.18k views

Framework Complexity Experiments Conclusion Performance and energy optimization of concurrent pipelined applications Anne Benoit, Paul Renaud-Goud and Yves Robert Institut Universitaire de France ROMA team, LIP Ecole Normale Sup

  1. Framework Complexity Experiments Conclusion Motivating example P = 3 3 + 8 3 = 539 Period: T = 3 Latency: L = 8 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 4/ 38

  2. Framework Complexity Experiments Conclusion Motivating example P = 3 3 + 8 3 = 539 Period: T = 3 Latency: L = 8 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 4/ 38

  3. Framework Complexity Experiments Conclusion Motivating example P = 3 3 + 8 3 = 539 Period: T = 3 Latency: L = 8 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 4/ 38

  4. Framework Complexity Experiments Conclusion Motivating example P = 539 P = 8 Period: T = 3 Latency: L = 8 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 4/ 38

  5. Framework Complexity Experiments Conclusion Motivating example P = 539 P = 8 Period: T = 3 T = 15 Latency: L = 8 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 4/ 38

  6. Framework Complexity Experiments Conclusion Motivating example P = 539 P = 8 Period: T = 3 T = 15 Latency: L = 8 L = 17 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 4/ 38

  7. Framework Complexity Experiments Conclusion Outline of the talk Framework 1 Application and platform Mapping rules Metrics Complexity results 2 Mono-criterion problems Bi-criteria problems Tri-criteria problems With resource sharing Experiments 3 Heuristics Experiments Summary Conclusion 4 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 5/ 38

  8. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Outline of the talk Framework 1 Application and platform Mapping rules Metrics Complexity results 2 Mono-criterion problems Bi-criteria problems Tri-criteria problems With resource sharing Experiments 3 Heuristics Experiments Summary Conclusion 4 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 6/ 38

  9. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Application model and execution platform Concurrent pipelined applications a ( i th stage of application a ) w i a : weight of stage S i δ i a : size of outcoming data of S i a Processors with multiple speeds (or modes): { s u , 1 , . . . , s u , m u } Constant speed during the execution Platform fully interconnected; b u , v : bandwidth between processors P u and P v ; overlap or non-overlap of communications and computations Three platform types: Fully homogeneous, or speed homogeneous Communication homogeneous, or speed heterogeneous Fully heterogeneous Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 7/ 38

  10. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Application model and execution platform Concurrent pipelined applications a ( i th stage of application a ) w i a : weight of stage S i δ i a : size of outcoming data of S i a Processors with multiple speeds (or modes): { s u , 1 , . . . , s u , m u } Constant speed during the execution Platform fully interconnected; b u , v : bandwidth between processors P u and P v ; overlap or non-overlap of communications and computations Three platform types: Fully homogeneous, or speed homogeneous Communication homogeneous, or speed heterogeneous Fully heterogeneous Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 7/ 38

  11. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Application model and execution platform Concurrent pipelined applications a ( i th stage of application a ) w i a : weight of stage S i δ i a : size of outcoming data of S i a Processors with multiple speeds (or modes): { s u , 1 , . . . , s u , m u } Constant speed during the execution Platform fully interconnected; b u , v : bandwidth between processors P u and P v ; overlap or non-overlap of communications and computations Three platform types: Fully homogeneous, or speed homogeneous Communication homogeneous, or speed heterogeneous Fully heterogeneous Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 7/ 38

  12. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Mapping rules Mapping with no processor sharing: relevant in practice (security rules) One-to-one mapping Interval mapping General mapping with resource sharing: better resource utilization Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 8/ 38

  13. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Mapping rules Mapping with no processor sharing: relevant in practice (security rules) One-to-one mapping Interval mapping General mapping with resource sharing: better resource utilization Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 8/ 38

  14. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Mapping rules Mapping with no processor sharing: relevant in practice (security rules) One-to-one mapping Interval mapping General mapping with resource sharing: better resource utilization Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 8/ 38

  15. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics without resource sharing Interval mapping on a single application with no resource sharing; k intervals I j of stages from S d j to S e j Period T of an application: minimum delay between the processing of two consecutive data sets � ej i = dj w i δ dj − 1 δ ej � � �� T ( overlap ) = max max , , j ∈{ 1 ,..., k } b alloc( dj − 1) , alloc( dj ) s alloc( dj ) b alloc( dj ) , alloc( ej +1) Latency L of an application: time, for a data set, to go through the whole pipeline   ej δ ej δ 0 m w i � � L = + +     b alloc(0) , alloc(1) s alloc( dj ) b alloc( dj ) , alloc( ej +1) j =1 i = dj Power P of the platform: sum of power of processors � P dyn ( s u ) = s α P = P ( u ) , P ( u ) = P dyn ( s u )+ P stat ( u ) , u , 2 ≤ α ≤ 3 P u Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 9/ 38

  16. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics without resource sharing Interval mapping on a single application with no resource sharing; k intervals I j of stages from S d j to S e j Period T of an application: minimum delay between the processing of two consecutive data sets � ej i = dj w i δ dj − 1 δ ej � � �� T ( overlap ) = max max , , j ∈{ 1 ,..., k } b alloc( dj − 1) , alloc( dj ) s alloc( dj ) b alloc( dj ) , alloc( ej +1) Latency L of an application: time, for a data set, to go through the whole pipeline   ej δ ej δ 0 m w i � � L = + +     b alloc(0) , alloc(1) s alloc( dj ) b alloc( dj ) , alloc( ej +1) j =1 i = dj Power P of the platform: sum of power of processors � P dyn ( s u ) = s α P = P ( u ) , P ( u ) = P dyn ( s u )+ P stat ( u ) , u , 2 ≤ α ≤ 3 P u Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 9/ 38

  17. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics without resource sharing Interval mapping on a single application with no resource sharing; k intervals I j of stages from S d j to S e j Period T of an application: minimum delay between the processing of two consecutive data sets � ej i = dj w i δ dj − 1 δ ej � � �� T ( overlap ) = max max , , j ∈{ 1 ,..., k } b alloc( dj − 1) , alloc( dj ) s alloc( dj ) b alloc( dj ) , alloc( ej +1) Latency L of an application: time, for a data set, to go through the whole pipeline   ej δ ej δ 0 m w i � � L = + +     b alloc(0) , alloc(1) s alloc( dj ) b alloc( dj ) , alloc( ej +1) j =1 i = dj Power P of the platform: sum of power of processors � P dyn ( s u ) = s α P = P ( u ) , P ( u ) = P dyn ( s u )+ P stat ( u ) , u , 2 ≤ α ≤ 3 P u Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 9/ 38

  18. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics without resource sharing Interval mapping on a single application with no resource sharing; k intervals I j of stages from S d j to S e j Period T of an application: minimum delay between the processing of two consecutive data sets � ej i = dj w i δ dj − 1 δ ej � � �� T ( overlap ) = max max , , j ∈{ 1 ,..., k } b alloc( dj − 1) , alloc( dj ) s alloc( dj ) b alloc( dj ) , alloc( ej +1) Latency L of an application: time, for a data set, to go through the whole pipeline   ej δ ej δ 0 m w i � � L = + +     b alloc(0) , alloc(1) s alloc( dj ) b alloc( dj ) , alloc( ej +1) j =1 i = dj Power P of the platform: sum of power of processors � P dyn ( s u ) = s α P = P ( u ) , P ( u ) = P dyn ( s u )+ P stat ( u ) , u , 2 ≤ α ≤ 3 P u Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 9/ 38

  19. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics with resource sharing With classical latency definition, NP-completeness of the execution scheduling, given a mapping with a period/latency objective ⇒ for general mappings, latency model of ¨ Ozg¨ uner: L = (2 m − 1) T , where m − 1 is the number of processor changes, and T the period of the application Period given ⇒ bound on number of processor changes Given an application, we can check if the mapping is valid, given a bound on period and latency per application: For period, check that each processor can handle its load computation and meet some communication constraints For latency, check the number of processor changes Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 10/ 38

  20. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics with resource sharing With classical latency definition, NP-completeness of the execution scheduling, given a mapping with a period/latency objective ⇒ for general mappings, latency model of ¨ Ozg¨ uner: L = (2 m − 1) T , where m − 1 is the number of processor changes, and T the period of the application Period given ⇒ bound on number of processor changes Given an application, we can check if the mapping is valid, given a bound on period and latency per application: For period, check that each processor can handle its load computation and meet some communication constraints For latency, check the number of processor changes Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 10/ 38

  21. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics with resource sharing With classical latency definition, NP-completeness of the execution scheduling, given a mapping with a period/latency objective ⇒ for general mappings, latency model of ¨ Ozg¨ uner: L = (2 m − 1) T , where m − 1 is the number of processor changes, and T the period of the application Period given ⇒ bound on number of processor changes Given an application, we can check if the mapping is valid, given a bound on period and latency per application: For period, check that each processor can handle its load computation and meet some communication constraints For latency, check the number of processor changes Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 10/ 38

  22. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics with resource sharing With classical latency definition, NP-completeness of the execution scheduling, given a mapping with a period/latency objective ⇒ for general mappings, latency model of ¨ Ozg¨ uner: L = (2 m − 1) T , where m − 1 is the number of processor changes, and T the period of the application Period given ⇒ bound on number of processor changes Given an application, we can check if the mapping is valid, given a bound on period and latency per application: For period, check that each processor can handle its load computation and meet some communication constraints For latency, check the number of processor changes Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 10/ 38

  23. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics with resource sharing With classical latency definition, NP-completeness of the execution scheduling, given a mapping with a period/latency objective ⇒ for general mappings, latency model of ¨ Ozg¨ uner: L = (2 m − 1) T , where m − 1 is the number of processor changes, and T the period of the application Period given ⇒ bound on number of processor changes Given an application, we can check if the mapping is valid, given a bound on period and latency per application: For period, check that each processor can handle its load computation and meet some communication constraints For latency, check the number of processor changes Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 10/ 38

  24. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Metrics with resource sharing With classical latency definition, NP-completeness of the execution scheduling, given a mapping with a period/latency objective ⇒ for general mappings, latency model of ¨ Ozg¨ uner: L = (2 m − 1) T , where m − 1 is the number of processor changes, and T the period of the application Period given ⇒ bound on number of processor changes Given an application, we can check if the mapping is valid, given a bound on period and latency per application: For period, check that each processor can handle its load computation and meet some communication constraints For latency, check the number of processor changes Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 10/ 38

  25. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Optimization problems Minimizing one criterion: Period or latency: minimize max a W a × T a or max a W a × L a Power: minimize P = � u P ( u ) Fixing one criterion: Fix the period or latency of each application → fix an array of periods or latencies Fix a bound on total power consumption P Multi-criteria approach: minimizing one criterion, fixing the other ones Energy criterion = power consumption, i.e., energy per time unit ⇒ combination power/period Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 11/ 38

  26. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Optimization problems Minimizing one criterion: Period or latency: minimize max a W a × T a or max a W a × L a Power: minimize P = � u P ( u ) Fixing one criterion: Fix the period or latency of each application → fix an array of periods or latencies Fix a bound on total power consumption P Multi-criteria approach: minimizing one criterion, fixing the other ones Energy criterion = power consumption, i.e., energy per time unit ⇒ combination power/period Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 11/ 38

  27. Framework Complexity Experiments Conclusion Application and platform Mapping rules Metrics Optimization problems Minimizing one criterion: Period or latency: minimize max a W a × T a or max a W a × L a Power: minimize P = � u P ( u ) Fixing one criterion: Fix the period or latency of each application → fix an array of periods or latencies Fix a bound on total power consumption P Multi-criteria approach: minimizing one criterion, fixing the other ones Energy criterion = power consumption, i.e., energy per time unit ⇒ combination power/period Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 11/ 38

  28. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Outline of the talk Framework 1 Application and platform Mapping rules Metrics Complexity results 2 Mono-criterion problems Bi-criteria problems Tri-criteria problems With resource sharing Experiments 3 Heuristics Experiments Summary Conclusion 4 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 12/ 38

  29. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Mono-criterion complexity results Period minimization: proc-hom proc-het special-app 1 com-hom com-hom com-het one-to-one polynomial (binary search) NP-complete interval polynomial NP-complete NP-complete Latency minimization: proc-hom proc-het special-app 1 com-hom com-hom com-het one-to-one polynomial NP-complete NP-complete interval polynomial (binary search) NP-complete 1 special-app: com-hom & pipe-hom Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 13/ 38

  30. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Mono-criterion complexity results Period minimization: proc-hom proc-het special-app 1 com-hom com-hom com-het one-to-one polynomial (binary search) NP-complete interval polynomial NP-complete NP-complete Latency minimization: proc-hom proc-het special-app 1 com-hom com-hom com-het one-to-one polynomial NP-complete NP-complete interval polynomial (binary search) NP-complete 1 special-app: com-hom & pipe-hom Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 13/ 38

  31. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Latency minimization (1) Problem: one-to-one mapping - many applications - heterogeneous platform - no communication - homogeneous pipelines - minimize max a L a Single application: greedy polynomial algorithm Many applications: reduction from 3-partition 3-partition : Input: 3 m + 1 integers a 1 , a 2 , . . . , a 3 m and B such that � i a i = mB Does there exist a partition I 1 , . . . , I m of { 1 , . . . , 3 m } such that for all j ∈ { 1 , . . . , m } , | I j | = 3 and � i ∈ I j a i = B ? Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 14/ 38

  32. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Latency minimization (2) 3-partition : renumbering of the a i such that:  a 1 , 1 + a 1 , 2 + a 1 , 3 = B   a 2 , 1 + a 2 , 2 + a 2 , 3 = B   . . .     a m , 1 + a m , 2 + a m , 3 = B Reduction: Can we obtain a latency L 0 ≤ B ? Equivalence of problems Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 15/ 38

  33. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Bi-criteria complexity results Period/latency minimization: proc-hom proc-het com-hom special-app com-hom com-het one-to-one or polynomial NP-complete interval Power/period minimization: proc-hom proc-het com-hom special-app com-hom com-het one-to-one polynomial (minimum matching) NP-complete interval polynomial NP-complete Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 16/ 38

  34. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Bi-criteria complexity results Period/latency minimization: proc-hom proc-het com-hom special-app com-hom com-het one-to-one or polynomial NP-complete interval Power/period minimization: proc-hom proc-het com-hom special-app com-hom com-het one-to-one polynomial (minimum matching) NP-complete interval polynomial NP-complete Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 16/ 38

  35. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Power/period minimization Problem: one-to-one mapping - many applications - communication homogeneous platform - power minimization for a given array of periods Minimum weighted matching of a bipartite graph Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 17/ 38

  36. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Bi-criteria complexity results Period/latency minimization: proc-hom proc-het com-hom special-app com-hom com-het one-to-one or polynomial NP-complete interval Power/period minimization: proc-hom proc-het com-hom special-app com-hom com-het one-to-one polynomial (minimum matching) NP-complete interval polynomial NP-complete Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 18/ 38

  37. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Single application (1) Problem: interval mapping - single application - fully homogeneous platform - power minimization for a given period P ( i , j , k ): minimum power to run stages S i to S j using exactly k processors → looking for min 1 ≤ k ≤ p P (1 , n , k ) Recurrence relation: P ( i , j , k ) = 1 ≤ ℓ ≤ j − 1 ( P ( i , ℓ, k − 1) + P ( ℓ + 1 , j , 1)) min Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 19/ 38

  38. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Single application (2) P ( i , i , q ) = + ∞ if q > 1 F j i : possible powers of a processor running the stages S i to S j , fulfilling the period constraint � � � � δ i − 1 � j k = i w k , δ j F j i = P dyn ( s ℓ ) + P stat , max b , ≤ T , ℓ ∈ { 1 , . . . , m } s ℓ b min F j if F j � i � = ∅ P ( i , j , 1) = i + ∞ otherwise Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 20/ 38

  39. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Many applications (1) Problem: interval mapping - fully homogeneous platform - power minimization for given periods by application P q a : minimum power consumed by q processors so that the period constraint on the application a is met, found by the previous dynamic programming P ( a , k ): minimum power consumed by k processors on the applications 1 , . . . , a , unknown P (1 , k ) = P k Initialization: ∀ k ∈ { 1 , . . . , p } 1 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 21/ 38

  40. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Many applications (2) P ( a − 1 , k − q ) + P q � � Recurrence: P ( a , k ) = min 1 ≤ q < k a Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 22/ 38

  41. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Tri-criteria complexity results proc-hom proc-het com-hom special-app com-hom com-het one-to-one or NP-complete interval Reduction from 2-partition n � (Instance of 2-partition : a 1 , a 2 , . . . , a n with σ = a i ) i =1 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 23/ 38

  42. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Problem instance One-to-one mapping - fully homogeneous platform P 0 = P ∗ + α X ( σ/ 2 + 1 / 2), L 0 = L ∗ − X ( σ/ 2 − 1 / 2), T 0 = L 0 where P ∗ and L ∗ are power and latency when each S i is run at speed s 2 i − 1 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 24/ 38

  43. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing Main ideas K big enough and X small enough so that the stage S i must be processed at speed s 2 i − 1 or s 2 i For a subset I of { 1 , . . . , n } , if ( S i is run at speed s 2 i ⇔ i ∈ I ), P = P ∗ + L = L ∗ − � � ( α a i X + o ( X )) , ( a i X − o ( X )) i ∈I i ∈I Recall: P 0 = P ∗ + α X ( σ/ 2 + 1 / 2) L 0 = L ∗ − X ( σ/ 2 − 1 / 2) , Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 25/ 38

  44. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing And for general mappings with resource sharing? Exhaustive complexity study with no resource sharing: new polynomial algorithms for multiple applications and results of NP-completeness With the simplified latency model, tri-criteria polynomial dynamic programming algorithm with no resource sharing and speed-homogeneous platforms With resource sharing or speed-heterogeneous platforms, all problem instances are NP-hard, even for only period minimization Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 26/ 38

  45. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing And for general mappings with resource sharing? Exhaustive complexity study with no resource sharing: new polynomial algorithms for multiple applications and results of NP-completeness With the simplified latency model, tri-criteria polynomial dynamic programming algorithm with no resource sharing and speed-homogeneous platforms With resource sharing or speed-heterogeneous platforms, all problem instances are NP-hard, even for only period minimization Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 26/ 38

  46. Framework Complexity Experiments Conclusion Mono-criterion Bi-criteria Tri-criteria With resource sharing And for general mappings with resource sharing? Exhaustive complexity study with no resource sharing: new polynomial algorithms for multiple applications and results of NP-completeness With the simplified latency model, tri-criteria polynomial dynamic programming algorithm with no resource sharing and speed-homogeneous platforms With resource sharing or speed-heterogeneous platforms, all problem instances are NP-hard, even for only period minimization Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 26/ 38

  47. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Outline of the talk Framework 1 Application and platform Mapping rules Metrics Complexity results 2 Mono-criterion problems Bi-criteria problems Tri-criteria problems With resource sharing Experiments 3 Heuristics Experiments Summary Conclusion 4 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 27/ 38

  48. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Heuristics Tri-criteria problem: power consumption minimization given a bound on period and latency per application, on speed heterogeneous platform Each heuristic (except H2) exists in two variants: interval mapping without resource sharing and general mapping with resource sharing in order to evaluate the impact of processor reuse Latency model of ¨ Ozg¨ uner: L = (2 m − 1) T H1: random cuts H2: one entire application per processor (assignment problem) H2-split: interval splitting H3: two-step heuristic: choose a speed distribution and find a valid mapping (variants on both steps) Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 28/ 38

  49. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Fix processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  50. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Mapping heuristic: find a valid maping Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  51. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Mapping heuristic: find a valid maping Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  52. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Mapping heuristic: find a valid maping Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  53. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  54. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  55. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  56. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  57. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  58. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  59. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  60. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  61. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  62. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  63. Framework Complexity Experiments Conclusion Heuristics Experiments Summary H3-energy Iterate the process: increase processor speeds Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 29/ 38

  64. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Experimental plan Integer linear program to assess the absolute performance of the heuristics on small instances Small instances: two or three applications, around 15 stages per application, around 8 processors Execution time on 30 small instances: less than one second for all heuristics, one week for the ILP Each heuristic and the ILP: variant without sharing (”-n”) and variant with sharing (”-r”) General behavior of heuristics Impact of resource sharing Scalability of heuristics Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 30/ 38

  65. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Experimental plan Integer linear program to assess the absolute performance of the heuristics on small instances Small instances: two or three applications, around 15 stages per application, around 8 processors Execution time on 30 small instances: less than one second for all heuristics, one week for the ILP Each heuristic and the ILP: variant without sharing (”-n”) and variant with sharing (”-r”) General behavior of heuristics Impact of resource sharing Scalability of heuristics Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 30/ 38

  66. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Experimental plan Integer linear program to assess the absolute performance of the heuristics on small instances Small instances: two or three applications, around 15 stages per application, around 8 processors Execution time on 30 small instances: less than one second for all heuristics, one week for the ILP Each heuristic and the ILP: variant without sharing (”-n”) and variant with sharing (”-r”) General behavior of heuristics Impact of resource sharing Scalability of heuristics Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 30/ 38

  67. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Increasing latency 1 0.8 0.6 1/Energy 0.4 0.2 0 3 4 5 6 7 8 9 10 11 12 nbInter cplex-r H2 H3-upDown-r H3-energy-r H1-r H2-split-r H3-speed-r best Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 31/ 38

  68. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Increasing number of processors 1 0.8 0.6 1/Energy 0.4 0.2 0 1 2 3 4 5 6 7 nbProcs cplex-r H2 H3-upDown-r H3-energy-r H1-r H2-split-r H3-speed-r best Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 32/ 38

  69. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Impact of static power 1.2 1.1 1 0.9 0.8 1/Energy 0.7 0.6 0.5 0.4 0.3 0.2 0 500 1000 1500 2000 max Estat cplex-n H1-r H2-split-n H3-upDown-n H1-n H2 H2-split-r H3-upDown-r Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 33/ 38

  70. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Impact of mode distribution 3 2.5 2 1/Energy 1.5 1 0.5 0 10 20 30 40 50 60 70 80 s u,l+1 - s u,l cplex-n H1-r H2-split-n H3-upDown-n H1-n H2 H2-split-r H3-upDown-r Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 34/ 38

  71. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Scalability 60000 50000 40000 Energy 30000 20000 10000 0 0 2 4 6 8 10 12 14 16 18 20 nbApp H1-r H2-split-r H3-speed-r best H2 H3-upDown-r H3-energy-r Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 35/ 38

  72. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Summary of experiments Efficient heuristics: best heuristic always at 90% of the optimal solution on small instances Supremacy of H2-split-r, better in average, and gets even better when problem instances get larger H3 has smaller execution time (one second versus three minutes for 20 applications), ILP not usable in practice Resource sharing becomes crucial with important static power (use fewer processors) or with distant modes (better use of all available speed) Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 36/ 38

  73. Framework Complexity Experiments Conclusion Heuristics Experiments Summary Summary of experiments Efficient heuristics: best heuristic always at 90% of the optimal solution on small instances Supremacy of H2-split-r, better in average, and gets even better when problem instances get larger H3 has smaller execution time (one second versus three minutes for 20 applications), ILP not usable in practice Resource sharing becomes crucial with important static power (use fewer processors) or with distant modes (better use of all available speed) Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 36/ 38

  74. Framework Complexity Experiments Conclusion Outline of the talk Framework 1 Application and platform Mapping rules Metrics Complexity results 2 Mono-criterion problems Bi-criteria problems Tri-criteria problems With resource sharing Experiments 3 Heuristics Experiments Summary Conclusion 4 Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 37/ 38

  75. Framework Complexity Experiments Conclusion Conclusion and future work Exhaustive complexity study new polynomial algorithms new NP-completeness proofs impact of model on complexity (tri-criteria homogeneous) Experimental study efficient heuristics impact of resource reuse Current/future work continuous speeds approximation algorithms Anne.Benoit@ens-lyon.fr CCGSC 2010 Performance and energy optimization 38/ 38

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Energy Optimization Stephan Wollenburg &amp; Katelyn Mazuera Agenda Energy Optimization (EO)

Energy Optimization Stephan Wollenburg &amp; Katelyn Mazuera Agenda Energy Optimization (EO)

Energy Optimization Stephan Wollenburg &amp; Katelyn Mazuera Agenda Energy Optimization (EO) Overview Then &amp; Now: Heating Equipment Fuel Neutral Opportunities for Residential Customers Online Calculator Trainings

344 views • 15 slides
PERFORMANCE OF PERFORMANCE OF OPTIMIZATION OPTIMIZATION ALGORITHMS ALGORITHMS FOR DERIVING

PERFORMANCE OF PERFORMANCE OF OPTIMIZATION OPTIMIZATION ALGORITHMS ALGORITHMS FOR DERIVING

PERFORMANCE OF PERFORMANCE OF OPTIMIZATION OPTIMIZATION ALGORITHMS ALGORITHMS FOR DERIVING MATERIAL DATA FROM BENCH SCALE TESTS Patrick Lauer University of Wuppertal lauer@uni-wuppertal.de Content 1. Content 2. Introduction 3. Method

490 views • 31 slides
PERFORMANCE OPTIMIZATION IN RED PERFORMANCE OPTIMIZATION IN RED HAT OPENSTACK PLATFORM HAT

PERFORMANCE OPTIMIZATION IN RED PERFORMANCE OPTIMIZATION IN RED HAT OPENSTACK PLATFORM HAT

PERFORMANCE OPTIMIZATION IN RED PERFORMANCE OPTIMIZATION IN RED HAT OPENSTACK PLATFORM HAT OPENSTACK PLATFORM LUNCH &amp; LEARN LUNCH &amp; LEARN Razique Mahroua Red Hat Training - Services Content Architect ABOUT ME ABOUT ME Course author

881 views • 68 slides
Web Performance Optimization: Analytics Wim Leers Promotor: Prof. dr. Jan Van den Bussche Web

Web Performance Optimization: Analytics Wim Leers Promotor: Prof. dr. Jan Van den Bussche Web

Web Performance Optimization: Analytics Wim Leers Promotor: Prof. dr. Jan Van den Bussche Web Performance Optimization Speed matters! Source: http://www.useit.com/alertbox/response-times.html, Jakob Nielsen, June 21, 2010 Web Performance

755 views • 59 slides
C&amp;I Implementation Update May 20, 2020 Agenda Introduction Continuous Energy

C&amp;I Implementation Update May 20, 2020 Agenda Introduction Continuous Energy

C&amp;I Implementation Update May 20, 2020 Agenda Introduction Continuous Energy Improvement Energy Optimization Equipment &amp; Systems Performance Optimization New Construction Lighting PA Priorities Comprehensive

770 views • 37 slides
Optimization of Scalable Concurrent Pool Based on Diffraction Trees Anenkov Alexandr Siberian

Optimization of Scalable Concurrent Pool Based on Diffraction Trees Anenkov Alexandr Siberian

Optimization of Scalable Concurrent Pool Based on Diffraction Trees Anenkov Alexandr Siberian State University of Telecommunications and Information Sciences, Novosibirsk E-mail: alex.anenkov@outlook.com Paznikov Alexey Saint Petersburg

708 views • 31 slides
1 Tuning MATLAB for Better Performance Tutorial Overview General advice about optimization

1 Tuning MATLAB for Better Performance Tutorial Overview General advice about optimization

1 Tuning MATLAB for Better Performance Tutorial Overview General advice about optimization A typical workflow for performance optimization MATLAB's performance measurement tools Common performance issues in MATLAB and how to solve

656 views • 29 slides
Energy Needs for Peak Performance Energy Needs for Peak Performance By: Stacey Sturzenacker,

Energy Needs for Peak Performance Energy Needs for Peak Performance By: Stacey Sturzenacker,

Energy Needs for Peak Performance Energy Needs for Peak Performance By: Stacey Sturzenacker, Rachel Robinson and Dani Rodriguez Objectives Describe what energy is and how it is expressed. Give an overview of the different types of

1.3k views • 53 slides
Tracking Building Energy Performance: The need to measure, track and benchmark energy performance

Tracking Building Energy Performance: The need to measure, track and benchmark energy performance

Tracking Building Energy Performance: The need to measure, track and benchmark energy performance for LEED Projects Presentation by Matt Arneson Peter Dahl, Sebesta Blomberg We will cover: What is energy benchmarking?

599 views • 28 slides
CONCURRENT COLLECTIONS 2 5/24/11 Concurrent Collec9ons

CONCURRENT COLLECTIONS 2 5/24/11 Concurrent Collec9ons

1 5/24/11 Concurrent Collec9ons CONCURRENT COLLECTIONS 2 5/24/11 Concurrent Collec9ons Acknowledgements Slides and material from Kathleen Knobe (Intel)

865 views • 20 slides
Outline Performance Optimization of Component-based Data Intensive Motivation Applications

Outline Performance Optimization of Component-based Data Intensive Motivation Applications

Outline Performance Optimization of Component-based Data Intensive Motivation Applications Approach Optimization Group Instances Alan Sussman Optimization Transparent Copies Michael Beynon Ongoing Work Tahsin Kurc

76 views • 6 slides
Performance Optimization Project 2 Lab Schedule Activities Assignments Due Today

Performance Optimization Project 2 Lab Schedule Activities Assignments Due Today

Computer Systems and Networks ECPE 170 University of the Pacific Performance Optimization Project 2 Lab Schedule Activities Assignments Due Today Today Lab 7 Performance Lab 5 due by 11:59pm Optimization

832 views • 22 slides
Goals of Program Optimization (1 of 2) Goal: Improve program performance within some constraints

Goals of Program Optimization (1 of 2) Goal: Improve program performance within some constraints

CS 426 Topic 9: Optimization Basics Goals of Program Optimization (1 of 2) Goal: Improve program performance within some constraints Ask Three Key Questions for Every Optimization 1. Is it legal? 2. Is it profitable? 3. Is it compile-time cost

413 views • 17 slides
Rela%vis%c Red Black Trees Rela%vis%c Programming Concurrent

Rela%vis%c Red Black Trees Rela%vis%c Programming Concurrent

Rela%vis%c Red Black Trees Rela%vis%c Programming Concurrent reading and wri%ng improves performance and scalability concurrent readers may disagree on the

771 views • 51 slides
Analysis Optimization (IESA-Opt) The LP optimization model of the energy system of the

Analysis Optimization (IESA-Opt) The LP optimization model of the energy system of the

Integrated Energy System Analysis Optimization (IESA-Opt) The LP optimization model of the energy system of the Netherlands Manuel Sanchez (manuel.sanchezdieguez@tno.nl) Amir Fattahi (amir.fattahi@tno.nl) PRESENTATION OVERVIEW Fir

483 views • 47 slides
Multiobjective Optimization Performance Measures in Many-Objective Optimization Facult: Eduardo

Multiobjective Optimization Performance Measures in Many-Objective Optimization Facult: Eduardo

Multiobjective Optimization Performance Measures in Many-Objective Optimization Facult: Eduardo G. Carrano Frederico G. Guimares Lucas S. Batista {egcarrano,fredericoguimaraes,lusoba}@ufmg.br www.ppgee.ufmg.br/ lusoba Universidade

229 views • 12 slides
An Early Evaluation of the Scalability of Graph Algorithms on the Intel MIC Architecture Erik

An Early Evaluation of the Scalability of Graph Algorithms on the Intel MIC Architecture Erik

An Early Evaluation of the Scalability of Graph Algorithms on the Intel MIC Architecture Erik Saule 1 and urek 1 , 2 Umit V. C ataly { esaule,umit } @bmi.osu.edu 1 Department of Biomedical Informatics 2 Department of Electrical and

486 views • 25 slides
Aaron Turon Mozilla Research C/C++ ML/Haskell Rust Safe systems programming Why

Aaron Turon Mozilla Research C/C++ ML/Haskell Rust Safe systems programming Why

Aaron Turon Mozilla Research C/C++ ML/Haskell Rust Safe systems programming Why Mozilla? Browsers need control . Browsers need safety . Servo: Next-generation browser built in Rust. C++ What is control? void example() {

2.01k views • 174 slides
Software Engineering I (02161) Week 5 Assoc. Prof. Hubert Baumeister Informatics and

Software Engineering I (02161) Week 5 Assoc. Prof. Hubert Baumeister Informatics and

Software Engineering I (02161) Week 5 Assoc. Prof. Hubert Baumeister Informatics and Mathematical Modelling Technical University of Denmark Spring 2011 2011 H. Baumeister (IMM) c Software Engineering I (02161) Spring 2011 5 / 65 Recap

617 views • 48 slides
INF580 Large-scale Mathematical Programming TD6 Random projections Leo Liberti CNRS

INF580 Large-scale Mathematical Programming TD6 Random projections Leo Liberti CNRS

INF580 Large-scale Mathematical Programming TD6 Random projections Leo Liberti CNRS LIX, Ecole Polytechnique, France 200227 Leo Liberti (CNRS LIX) INF580 / TD6 200227 1 / 41 Do you believe in the JLL? Outline Do you believe in

1.52k views • 41 slides
Understanding your responsibilities as an employer of PAs Welcome This webinar is being

Understanding your responsibilities as an employer of PAs Welcome This webinar is being

Understanding your responsibilities as an employer of PAs Welcome This webinar is being recorded for others to watch. Attendees are on mute. Please do chat, comment and ask questions via the Questions function, this is

632 views • 37 slides
SUPERVISION OF A PRO BONO CLINIC Vicky Ling Founder member of the Law Consultancy Network

SUPERVISION OF A PRO BONO CLINIC Vicky Ling Founder member of the Law Consultancy Network

SUPERVISION OF A PRO BONO CLINIC Vicky Ling Founder member of the Law Consultancy Network www.lawconsultancynetwork.co.uk SUPERVISION - A DEFINITION The action or process of watching and directing what someone does or how something is

288 views • 15 slides
8 th Annual University of Toronto Patent Colloquium Non-Infringing Alternatives Sandon Shogilev,

8 th Annual University of Toronto Patent Colloquium Non-Infringing Alternatives Sandon Shogilev,

8 th Annual University of Toronto Patent Colloquium Non-Infringing Alternatives Sandon Shogilev, Partner Goodmans LLP November 15, 2019 Remedies for Patent Infringement Subsection 55(1) of the Patent Act provides that a person who

326 views • 13 slides
Genetic Testing of Children for the Sake of Other Family Members Eiji Maruyama Kobe University

Genetic Testing of Children for the Sake of Other Family Members Eiji Maruyama Kobe University

Genetic Testing of Children for the Sake of Other Family Members Eiji Maruyama Kobe University School of Law Introduction In this presentation, I would like to discuss the ethical and legal problems of genetic testing of minors for the sake

448 views • 17 slides

More recommend