Introduction Framework Examples Complexity Conclusion Optimizing Latency and Reliability of Pipeline Workflow Applications Anne Benoit Veronika Rehn-Sonigo Yves Robert GRAAL team, LIP ´ Ecole Normale Sup´ erieure de Lyon France HCW 2008 Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 1/ 27
Introduction Framework Examples Complexity Conclusion Introduction and motivation Mapping applications onto parallel platforms Difficult challenge Heterogeneous clusters, fully heterogeneous platforms Even more difficult! Structured programming approach Easier to program (deadlocks, process starvation) Range of well-known paradigms (pipeline, farm) Algorithmic skeleton: help for mapping Mapping pipeline skeletons onto heterogeneous platforms Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 2/ 27
Introduction Framework Examples Complexity Conclusion Introduction and motivation Mapping applications onto parallel platforms Difficult challenge Heterogeneous clusters, fully heterogeneous platforms Even more difficult! Structured programming approach Easier to program (deadlocks, process starvation) Range of well-known paradigms (pipeline, farm) Algorithmic skeleton: help for mapping Mapping pipeline skeletons onto heterogeneous platforms Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 2/ 27
Introduction Framework Examples Complexity Conclusion Introduction and motivation Mapping applications onto parallel platforms Difficult challenge Heterogeneous clusters, fully heterogeneous platforms Even more difficult! Structured programming approach Easier to program (deadlocks, process starvation) Range of well-known paradigms (pipeline, farm) Algorithmic skeleton: help for mapping Mapping pipeline skeletons onto heterogeneous platforms Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 2/ 27
Introduction Framework Examples Complexity Conclusion Multi-criteria scheduling of workflows Workflow Several consecutive data-sets enter the application graph. Multi-criteria? Latency: maximal time elapsed between beginning and end of execution of a data set Failure: the probability that a processor fails during execution Bi-criteria! Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 3/ 27
Introduction Framework Examples Complexity Conclusion Multi-criteria scheduling of workflows Workflow Several consecutive data-sets enter the application graph. Multi-criteria? Latency: maximal time elapsed between beginning and end of execution of a data set Failure: the probability that a processor fails during execution Bi-criteria! Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 3/ 27
Introduction Framework Examples Complexity Conclusion Multi-criteria scheduling of workflows Workflow Several consecutive data-sets enter the application graph. Multi-criteria? Latency: maximal time elapsed between beginning and end of execution of a data set Failure: the probability that a processor fails during execution Bi-criteria! Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 3/ 27
Introduction Framework Examples Complexity Conclusion Multi-criteria scheduling of workflows Workflow Several consecutive data-sets enter the application graph. Multi-criteria? Latency: maximal time elapsed between beginning and end of execution of a data set Failure: the probability that a processor fails during execution Bi-criteria! Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 3/ 27
Introduction Framework Examples Complexity Conclusion Rule of the game Map each pipeline stage on a single processor Goal: minimize latency AND minimize failure probability Several mapping strategies S 1 S 2 S k S n ... ... The pipeline application Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 4/ 27
Introduction Framework Examples Complexity Conclusion Rule of the game Map each pipeline stage on a single processor Goal: minimize latency AND minimize failure probability Several mapping strategies S 1 S 2 S k S n ... ... The pipeline application Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 4/ 27
Introduction Framework Examples Complexity Conclusion Rule of the game Map each pipeline stage on a single processor Goal: minimize latency AND minimize failure probability Several mapping strategies S 1 S 2 S k S n ... ... One-to-one Mapping Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 4/ 27
Introduction Framework Examples Complexity Conclusion Rule of the game Map each pipeline stage on a single processor Goal: minimize latency AND minimize failure probability Several mapping strategies S 1 S 2 S k S n ... ... Interval Mapping Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 4/ 27
Introduction Framework Examples Complexity Conclusion Rule of the game Map each pipeline stage on a single processor Goal: minimize latency AND minimize failure probability Several mapping strategies S 1 S 2 S k S n ... ... General Mapping Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 4/ 27
Introduction Framework Examples Complexity Conclusion Rule of the game Map each pipeline stage on a single processor Goal: minimize latency AND minimize failure probability Several mapping strategies S 1 S 2 S k S n ... ... Interval Mapping Replication (one interval onto several processors) in order to increase reliability Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 4/ 27
Introduction Framework Examples Complexity Conclusion Major Contributions Definition of bi-criteria mapping Complexity results Mono-criterion problems Bi-criteria problems Optimal algorithms Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 5/ 27
Introduction Framework Examples Complexity Conclusion Outline Framework 1 Motivating Examples 2 Complexity Results 3 Mono-criterion Problems Bi-criteria Problems Conclusion 4 Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 6/ 27
Introduction Framework Examples Complexity Conclusion The application δ 0 δ 1 δ k − 1 δ k δ n S 1 S 2 S k S n ... ... w 1 w 2 w k w n n stages S k , 1 ≤ k ≤ n S k : receives input of size δ k − 1 from S k − 1 performs w k computations outputs data of size δ k to S k +1 S 0 and S n +1 : virtual stages representing the outside world Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 7/ 27
Introduction Framework Examples Complexity Conclusion The platform s in P in P out s out b v , out b in , u P u P v b u , v s u s v p processors P u , 1 ≤ u ≤ p, fully interconnected s u : speed of processor P u bidirectional link link u , v : P u → P v , bandwidth b u , v fp u : failure probability of processor P u (independent of duration, meant to run for a long time) one-port model: each processor can either send, receive or compute at any time-step Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 8/ 27
Introduction Framework Examples Complexity Conclusion Different platforms Fully Homogeneous – Identical processors (s u = s) and links (b u , v = b): typical parallel machines Communication Homogeneous – Different-speed processors (s u � = s v ), identical links (b u , v = b): networks of workstations, clusters Fully Heterogeneous – Fully heterogeneous architectures, s u � = s v and b u , v � = b u ′ , v ′ : hierarchical platforms, grids Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 9/ 27
Introduction Framework Examples Complexity Conclusion Different platforms Fully Homogeneous – Identical processors (s u = s) and links (b u , v = b): typical parallel machines Failure Homogeneous – Identically reliable processors (fp u = fp v ) Communication Homogeneous – Different-speed processors (s u � = s v ), identical links (b u , v = b): networks of workstations, clusters Fully Heterogeneous – Fully heterogeneous architectures, s u � = s v and b u , v � = b u ′ , v ′ : hierarchical platforms, grids Failure Heterogeneous – Different failure probabilities (fp u � = fp v ) Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 9/ 27
Introduction Framework Examples Complexity Conclusion Mapping problem: Interval Mapping Partition of [1 .. n] into m intervals I j = [ d j , e j ] (with d j ≤ e j for 1 ≤ j ≤ m , d 1 = 1, d j +1 = e j + 1 for 1 ≤ j ≤ m − 1 and e m = n) Interval I j mapped onto set of processors P alloc( j ) � � FP = 1 − (1 − fp u ) 1 ≤ j ≤ p u ∈ alloc( j ) Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 10/ 27
Introduction Framework Examples Complexity Conclusion Mapping problem: Interval Mapping Partition of [1 .. n] into m intervals I j = [ d j , e j ] (with d j ≤ e j for 1 ≤ j ≤ m , d 1 = 1, d j +1 = e j + 1 for 1 ≤ j ≤ m − 1 and e m = n) Interval I j mapped onto set of processors P alloc( j ) � � FP = 1 − (1 − fp u ) 1 ≤ j ≤ p u ∈ alloc( j ) Veronika.Sonigo@ens-lyon.fr HCW 2008 Optimizing Latency and Reliability 10/ 27
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