A New Approach for Task Level Computational Resource Bi-Partitioning

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A New Approach for Task Level Computational
Resource Bi-Partitioning

• Gang Wang, Wenrui Gong, Ryan Kastner Express Lab,
  Dept. of ECE,
• University of California, Santa Barbara

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Overview

• Resource Partitioning Problem
• Ant System (AS) Heuristic
• AS for Task Level Resource Partitioning
• Experiment Results
• Future Work

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Resource Partitioning Problem(1)

• Heterogeneous architecture is getting more and
  more popular
• Partitioning problem is a fundamental challenge
• Automatically assign application onto different
  computation resources
• Optimizing system performance under constraints
• Two resource case hardware/software co-design

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Resource Partitioning Problem(2)

• NP-hard
• Different heuristic methods have been developed
• Simulated annealing
• Genetic Algorithms
• Tabu Search
• Expert System
• Kernighan/Lin

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Overview

• Resource Partitioning Problem
• Ant System (AS) Heuristic
• AS for Task Level Resource Partitioning
• Experiment Results
• Future Work

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Ant System Heuristic (1)

• First introduced for optimization problems by
  Dorigo et. al. 1996
• Inspired by ethological study on the behavior of
  ants Goss et. al. 1989
• A meta heuristic
• A multi-agent cooperative searching method
• A new way for combining global/local heuristics

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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Ant System Heuristic (2)
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Key Observations

• Autocatalytic effect
• Indirect communication (stigmergy)
• Ants deposit pheromones on the ground
• different the quality of the paths
• Pheromone trails encode a long-term global memory
  about the search process
• When the ants reach a decision, they are biased
  by the amount of pheromone (maybe
  probabilistically )

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Overview

• Resource Partitioning Problem
• Ant System (AS) Heuristic
• AS for Task Level Resource Partitioning
• Experiment Results
• Future Work

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AS Algorithm for HW/SW Co-Design

• Problem For a given application, find the
  optimal resource partition under certain system
  constraints
• Task level abstraction
• Task can map to GPP or Configurable Logic
• Pre-knowledge about the computational resources

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Modeling the Task/Resource Partitioning Problem

• Application is modeled as Task Graph (DAG)
• Sequential scheduling (not pipelined)

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Partitioning as Graph Bi-coloring

• Task 1, 2, 7 and 8 are assigned to the GPP
• Task 3, 4, and 6 onto the configurable logic
• The inbound edges are colored accordingly
• We dont care the coloring for virtual nodes t0
  and tn
• We dont care the coloring for edge e8n

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Partitioning as Graph Bi-coloring

• Each computing resource is assigned with a color
  ck
• Each edge eij is associated with a set of global
  heuristics (pheromone trails) ?ij(k) indicating
  the favorableness for tj to be colored with ck
• A coherent coloring is defined as
• Each task node in the DAG is colored
• All the inbound edges of a task node have the
  same coloring as that of the corresponding task
  node

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AS algorithm for resource partitioning (1)

1. Initially, assign each of the edges in the task
   graph with a fixed pheromone ?0 for both color c1
   and c2, where c1 corresponds to GPP, while c2 for
   the configurable logic
2. Put m ants on t0
3. Each ant traverses the task graph to create a
   feasible bi-coloring solution si for the task
   graph, where i 1, . . . ,m
4. Evaluate all the m solutions. The quality of the
   solution s is measured by the overall execution
   time time(s). Among all solutions, find the best
   solution sbest which provides the minimum
   execution time and satisfies the configurable
   logic area constraint

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AS algorithm for resource partitioning (2)

• Update the pheromone for each color on the edges
  as follows
• ?ij(k) ? (1 - ?)?ij(k) ??ij(k)
  (1)
• where
• 0 lt ? lt 1 is the evaporation ratio, escape from
  local minima
• k 1 or 2,
• ??ij(k) Q/time(sbest ) if eij is colored with
  ck in sbest
• 0 otherwise
• If the ending condition is reached, stop and
  report the best solution found. Otherwise go to
  step 2.

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Step 3 How to construct individual coloring

• Each ant traverses the graph in topologically
  sorted order
• Guarantees that each inbound edge to the current
  node has been already examined
• At each node, the ant will
• Make guesses for the coloring of the successor
  nodes
• Make decision on the coloring of the current node

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Make guesses for the successor task nodes

• At task node ti, the ant makes guesses the
  coloring for each of the successor nodes tj
• ?ij(k) global heuristic on coloring tj with ck
  
• ?j(k) local heuristic on coloring tj with ck

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Make decision on the coloring of the current node

• Upon entering a new task node ti, the ant makes a
  decision on the coloring of ti
• probabilistically based on the guesses made by
  all the immediate precedents of ti
• Inbound edges are correspondingly colored once
  this decision is made

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Find the best and update the pheromone trails
based on the solutions quality
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Extensibility

• Easy to extend to multi-way partitioning
• Different performance/constraint pair
• Different task level cost model

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Overview

• Resource Partitioning Problem
• Ant System (AS) Heuristic
• AS for Task Level Resource Partitioning
• Experiment Results
• Future Work

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Experiment System (1)

• Target system contains
• One GPP ( PowerPC 405 RISC)
• One configurable logic (Xilinx Virtex II with
  1232 CLBs)
• Sequential scheduling
• Precedence level has to be respected
• Tasks without precedence constraint can run
  concurrently given the resource partitioning
  allows

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Experiment System (2)

• Testing benchmark
• DAGs of different sizes are generated randomly
  with average branching factor of 5
• Real functions (in C/C) extracted from the
  MediaBench suits are mapped onto the task nodes
• Tasks are analyzed using SUIF and Machine SUIF
  tools to achieve detailed CDFG level description
• Simplified communication interface between tasks
• Goal Find the optimal resource partition that
  achieves the best worst case execution time under
  FPGA area constraint

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Evaluating AS algorithm

• Compare the AS results with
• Brute force search
• Offers definitive measurement for the quality
• Theoretical performance for Random Sampling
• Helps to filter out EASY test cases
• Stimulated annealing
• Popularly used
• Allow much bigger problem size

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Experiment Settings

• Each DAG has 25 task nodes, over 33 million
  possible assignments!
• 50 testing instances are generated originally
• After filtering out the easy cases using the
  brute force search, 25 difficult testing cases
  left
• Number of ants is set to 5, which equals to the
  average branching factor of the task graph
• Force AS algorithm stop after 100 iterations in
  each run

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Typical ant search run
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Result Quality Assessment (I)

• 91.7 of the results are within the top 3

• 77 of the results of AS are within the top 2

• 63.5 of the results are within top 0.1

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Result Quality Assessment (II)

• The absolute performance of the majority of the
  results found by AS are within 10 range
  comparing with the optimal

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Result Quality Assessment (III)

• The ability for finding one of the optimal
  partitions
• 460 times for 2,500 instances (18.4)
• While random sampling approach with the same
  computation time only has a chance of 8.5E-7
• For significant portion (gt20) of the tested
  examples, AS discovers the optimal partition with
  probability gt1/2

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Result Quality Assessment (IV)Multi-way SA

• Extended to the 3-way partitioning problem
• 33 difficult testing cases
• 325 possible partitions
• SA-50 has comparable run time as the AS
• SA-500 and SA-1000 runs at 10 and 20 times

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Contributions

• For the first time, introduced AS heuristic for
  HW/SW co-design problem
• Constructed a novel AS algorithm that achieved
  robust results that are qualitatively close to
  the optimal with minor computational cost for the
  testing benchmark
• Provided definitive quality assessment by
  comparing the proposed algorithm with the
  theoretical random sampling results
• Experiments shows the proposed algorithm
  surpasses popularly used SA heuristic

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Future work

• Extend to the multi-way resource partitioning
  problem ?
• More comprehensive comparison with other
  heuristic methods (such as GA, Tabu) ?
• Hybrid approach (e.g. AS followed by SA) ?
• Applying to more realistic and complex system
  model, e.g. more realistic communication model
• Extend AS from static partitioning to dynamic
  partitioning problem ( truly reconfigurable)

Thanks the your attention. Questions?